Abstract
Let
Let
J. C. Evard and F. Jafari, “On semigroups of operators on Hardy spaces,” preprint, 1995.
View at: Google ScholarA. G. Siskakis, “Weighted composition semigroups on Hardy spaces,” Linear Algebra and Its Applications, vol. 84, pp. 359–371, 1986.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. G. Siskakis, “Semigroups of composition operators on spaces of analytic functions, a review,” in Studies on Composition Operators (Laramie, WY, 1996), vol. 213 of Contemporary Mathematics, pp. 229–252, American Mathematical Society, Providence, RI, USA, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. de Leeuw, W. Rudin, and J. Wermer, “The isometries of some function spaces,” Proceedings of the American Mathematical Society, vol. 11, no. 5, pp. 694–698, 1960.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Nagasawa, “Isomorphisms between commutative Banach algebras with an application to rings of analytic functions,” Kōdai Mathematical Seminar Reports, vol. 11, pp. 182–188, 1959.
View at: Google Scholar | Zentralblatt MATH | MathSciNetF. Forelli, “The isometries of ,” Canadian Journal of Mathematics, vol. 16, pp. 721–728, 1964.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Cambern and K. Jarosz, “The isometries of ,” Proceedings of the American Mathematical Society, vol. 107, no. 1, pp. 205–214, 1989.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetC. J. Kolaski, “Surjective isometries of weighted Bergman spaces,” Proceedings of the American Mathematical Society, vol. 105, no. 3, pp. 652–657, 1989.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetT. Mazur, “Canonical isometry on weighted Bergman spaces,” Pacific Journal of Mathematics, vol. 136, no. 2, pp. 303–310, 1989.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP.-K. Lin, “The isometries of ,” Pacific Journal of Mathematics, vol. 143, no. 1, pp. 69–77, 1990.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. Arveson, “Subalgebras of -algebras—III: multivariable operator theory,” Acta Mathematica, vol. 181, no. 2, pp. 159–228, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. R. M. Attele, “Analytic multipliers of Bergman spaces,” The Michigan Mathematical Journal, vol. 31, no. 3, pp. 307–319, 1984.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Axler, “Multiplication operators on Bergman spaces,” Journal für die reine und angewandte Mathematik, vol. 336, pp. 26–44, 1982.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Axler, “Zero multipliers of Bergman spaces,” Canadian Mathematical Bulletin, vol. 28, no. 2, pp. 237–242, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Axler, “The Bergman space, the Bloch space, and commutators of multiplication operators,” Duke Mathematical Journal, vol. 53, no. 2, pp. 315–332, 1986.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Axler and A. L. Shields, “Univalent multipliers of the Dirichlet space,” The Michigan Mathematical Journal, vol. 32, no. 1, pp. 65–80, 1985.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. Bercovici, “The algebra of multiplication operators on Bergman spaces,” Archiv der Mathematik, vol. 48, no. 2, pp. 165–174, 1987.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Eschmeier, “Multiplication operators on Bergman spaces are reflexive,” in Linear Operators in Function Spaces (Timişoara, 1988), H. Helson, B. Sz-Nagy, F.-H. Vasilescu, and Gr. Arsene, Eds., vol. 43 of Operator Theory Adv. Appl., pp. 165–184, Birkhäuser, Basel, Switzerland, 1990.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. H. Luecking, “Multipliers of Bergman spaces into Lebesgue spaces,” Proceedings of the Edinburgh Mathematical Society, vol. 29, no. 1, pp. 125–131, 1986.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. Vukotić, “Pointwise multiplication operators between Bergman spaces on simply connected domains,” Indiana University Mathematics Journal, vol. 48, no. 3, pp. 793–803, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Zhu, “A trace formula for multiplication operators on invariant subspaces of the Bergman space,” Integral Equations and Operator Theory, vol. 40, no. 2, pp. 244–255, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. M. Campbell and R. J. Leach, “A survey of multipliers as related to classical function theory,” Complex Variables, vol. 3, no. 1–3, pp. 85–111, 1984.
View at: Google Scholar | Zentralblatt MATH | MathSciNetN. S. Feldman, “Pointwise multipliers from the Hardy space to the Bergman space,” Illinois Journal of Mathematics, vol. 43, no. 2, pp. 211–221, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Ohno and H. Takagi, “Some properties of weighted composition operators on algebras of analytic functions,” Journal of Nonlinear and Convex Analysis, vol. 2, no. 3, pp. 369–380, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Arazy, Multipliers of Bloch Functions, vol. 54, University of Haifa Mathematics, Haifa, Israel, 1982.
View at: Google ScholarL. Brown and A. L. Shields, “Multipliers and cyclic vectors in the Bloch space,” The Michigan Mathematical Journal, vol. 38, no. 1, pp. 141–146, 1991.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. A. Stegenga, “Multipliers of the Dirichlet space,” Illinois Journal of Mathematics, vol. 24, no. 1, pp. 113–139, 1980.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. M. Ortega and J. Fàbrega, “Pointwise multipliers and corona type decomposition in BMOA,” Annales de l'Institut Fourier, vol. 46, no. 1, pp. 111–137, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNetH. Jarchow, V. Montesinos, K. J. Wirths, and J. Xiao, “Duality for some large spaces of analytic functions,” Proceedings of the Edinburgh Mathematical Society, vol. 44, no. 3, pp. 571–583, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetN. Yanagihara, “Multipliers and linear functionals for the class ,” Transactions of the American Mathematical Society, vol. 180, pp. 449–461, 1973.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Bonet, P. Domański, and M. Lindström, “Pointwise multiplication operators on weighted Banach spaces of analytic functions,” Studia Mathematica, vol. 137, no. 2, pp. 177–194, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Bonet, P. Domański, M. Lindström, and J. Taskinen, “Composition operators between weighted Banach spaces of analytic functions,” Journal of Australian Mathematical Society, vol. 64, no. 1, pp. 101–118, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Bonet, P. Domański, and M. Lindström, “Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions,” Canadian Mathematical Bulletin, vol. 42, no. 2, pp. 139–148, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Bonet, P. Domański, and M. Lindström, “Weakly compact composition operators on analytic vector-valued function spaces,” Annales Academiæ Scientiarium Fennicæ. Mathematica, vol. 26, no. 1, pp. 233–248, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. D. Contreras and A. G. Hernández-Díaz, “Weighted composition operators in weighted Banach spaces of analytic functions,” Journal of Australian Mathematical Society, vol. 69, no. 1, pp. 41–60, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. L. Shields and D. L. Williams, “Bonded projections, duality, and multipliers in spaces of analytic functions,” Transactions of the American Mathematical Society, vol. 162, pp. 287–302, 1971.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. L. Shields and D. L. Williams, “Bounded projections, duality, and multipliers in spaces of harmonic functions,” Journal für die reine und angewandte Mathematik, vol. 299/300, pp. 256–279, 1978.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. D. Contreras and A. G. Hernández-Díaz, “Weighted composition operators on Hardy spaces,” Journal of Mathematical Analysis and Applications, vol. 263, no. 1, pp. 224–233, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG. Mirzakarimi and K. Seddighi, “Weighted composition operators on Bergman and Dirichlet spaces,” Georgian Mathematical Journal, vol. 4, no. 4, pp. 373–383, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetB. D. MacCluer and R. Zhao, “Essential norms of weighted composition operators between Bloch-type spaces,” The Rocky Mountain Journal of Mathematics, vol. 33, no. 4, pp. 1437–1458, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Ohno, “Weighted composition operators between and the Bloch space,” Taiwanese Journal of Mathematics, vol. 5, no. 3, pp. 555–563, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Ohno and R. Zhao, “Weighted composition operators on the Bloch space,” Bulletin of the Australian Mathematical Society, vol. 63, no. 2, pp. 177–185, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Ohno, K. Stroethoff, and R. Zhao, “Weighted composition operators between Bloch-type spaces,” The Rocky Mountain Journal of Mathematics, vol. 33, no. 1, pp. 191–215, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Montes-Rodríguez, “Weighted composition operators on weighted Banach spaces of analytic functions,” Journal of the London Mathematical Society, vol. 61, no. 3, pp. 872–884, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetF. Jafari, T. Tonev, E. Toneva, and K. Yale, “Holomorphic flows, cocycles, and coboundaries,” The Michigan Mathematical Journal, vol. 44, no. 2, pp. 239–253, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetC. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. H. Shapiro, Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics, Springer, New York, NY, USA, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. K. Singh and J. S. Manhas, Composition Operators on Function Spaces, vol. 179 of North-Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. D. Bierstedt, J. Bonet, and A. Galbis, “Weighted spaces of holomorphic functions on balanced domains,” The Michigan Mathematical Journal, vol. 40, no. 2, pp. 271–297, 1993.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. D. Bierstedt, J. Bonet, and J. Taskinen, “Associated weights and spaces of holomorphic functions,” Studia Mathematica, vol. 127, no. 2, pp. 137–168, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. D. Bierstedt and W. H. Summers, “Biduals of weighted Banach spaces of analytic functions,” Journal of Australian Mathematical Society, vol. 54, no. 1, pp. 70–79, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Galbis, “Weighted Banach spaces of entire functions,” Archiv der Mathematik, vol. 62, no. 1, pp. 58–64, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. García, M. Maestre, and P. Sevilla-Peris, “Composition operators between weighted spaces of holomorphic functions on Banach spaces,” Annales Academiæ Scientiarium Fennicæ. Mathematica, vol. 29, no. 1, pp. 81–98, 2004.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. Lusky, “On weighted spaces of harmonic and holomorphic functions,” Journal of the London Mathematical Society, vol. 51, no. 2, pp. 309–320, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Burbea and P. Masani, Banach and Hilbert Spaces of Vector-Valued Functions, vol. 90 of Research Notes in Mathematics, Pitman, Boston, Mass, USA, 1984.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. B. Garnett, Bounded Analytic Functions, vol. 96 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1981.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Grothendieck, Topological Vector Spaces, Gordon and Breach Science, New York, NY, USA, 1992.
View at: Google Scholar | Zentralblatt MATHW. Rudin, Functional Analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill, New York, NY, USA, 1973.
View at: Google Scholar | Zentralblatt MATH | MathSciNetL. A. Rubel and A. L. Shields, “The second duals of certain spaces of analytic functions,” Journal of Australian Mathematical Society, vol. 11, pp. 276–280, 1970.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. S. Manhas, “Multiplication operators on weighted locally convex spaces of vector-valued analytic functions,” Southeast Asian Bulletin of Mathematics, vol. 27, no. 4, pp. 649–660, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Cichoń and K. Seip, “Weighted holomorphic spaces with trivial closed range multiplication operators,” Proceedings of the American Mathematical Society, vol. 131, no. 1, pp. 201–207, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. K. Singh and J. S. Manhas, “Invertible composition operators on weighted function spaces,” Acta Scientiarum Mathematicarum, vol. 59, no. 3-4, pp. 489–501, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Pietsch, Operator Ideals, vol. 16 of Mathematical Monographs, VEB Deutscher Verlag der Wissenschaften, Berlin, Germany, 1978.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Rueda, “On the Banach-Dieudonné theorem for spaces of holomorphic functions,” Quaestiones Mathematicae, vol. 19, no. 1-2, pp. 341–352, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. García, M. Maestre, and P. Rueda, “Weighted spaces of holomorphic functions on Banach spaces,” Studia Mathematica, vol. 138, no. 1, pp. 1–24, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. S. Manhas, “Homomorphisms and composition operators on weighted spaces of analytic functions,” preprint, 2006.
View at: Google ScholarR. Aron, P. Galindo, and M. Lindström, “Compact homomorphisms between algebras of analytic functions,” Studia Mathematica, vol. 123, no. 3, pp. 235–247, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Galindo, M. Lindström, and R. Ryan, “Weakly compact composition operators between algebras of bounded analytic functions,” Proceedings of the American Mathematical Society, vol. 128, no. 1, pp. 149–155, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Bonet and M. Friz, “Weakly compact composition operators on locally convex spaces,” Mathematische Nachrichten, vol. 245, no. 1, pp. 26–44, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet