About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 501592, 9 pages
http://dx.doi.org/10.1155/2013/501592
Research Article

Weighted Vector-Valued Holomorphic Functions on Banach Spaces

Escuela Politécnica Superior de Alcoy, IUMPA, Universitat Politècnica de València, Plaza Ferrándiz y Carbonell 1, 03801 Alcoy, Spain

Received 11 February 2013; Accepted 14 May 2013

Academic Editor: Anna Mercaldo

Copyright © 2013 Enrique Jordá. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Dunford, “Uniformity in linear spaces,” Transactions of the American Mathematical Society, vol. 44, no. 2, pp. 305–356, 1938. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Grothendieck, “Sur certains espaces de fonctions holomorphes. I,” Journal für die Reine und Angewandte Mathematik, vol. 192, pp. 35–64, 1953. View at Zentralblatt MATH · View at MathSciNet
  3. W. M. Bogdanowicz, “Analytic continuation of holomorphic functions with values in a locally convex space,” Proceedings of the American Mathematical Society, vol. 22, pp. 660–666, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. W. Arendt and N. Nikolski, “Vector-valued holomorphic functions revisited,” Mathematische Zeitschrift, vol. 234, no. 4, pp. 777–805, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Bonet, L. Frerick, and E. Jordá, “Extension of vector-valued holomorphic and harmonic functions,” Studia Mathematica, vol. 183, no. 3, pp. 225–248, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. Frerick and E. Jordá, “Extension of vector-valued functions,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 14, no. 3, pp. 499–507, 2007. View at Zentralblatt MATH · View at MathSciNet
  7. L. Frerick, E. Jordá, and J. Wengenroth, “Extension of bounded vector-valued functions,” Mathematische Nachrichten, vol. 282, no. 5, pp. 690–696, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. K.-G. Grosse-Erdmann, “A weak criterion for vector-valued holomorphy,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 136, no. 2, pp. 399–411, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Laitila and H.-O. Tylli, “Composition operators on vector-valued harmonic functions and Cauchy transforms,” Indiana University Mathematics Journal, vol. 55, no. 2, pp. 719–746, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. J. Beltrán, “Linearization of weighted (LB)-spaces of entire functions on Banach spaces,” Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales A, vol. 106, no. 2, pp. 275–286, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. D. Carando and I. Zalduendo, “Linearization of functions,” Mathematische Annalen, vol. 328, no. 4, pp. 683–700, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Mujica, “Linearization of bounded holomorphic mappings on Banach spaces,” Transactions of the American Mathematical Society, vol. 324, no. 2, pp. 867–887, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K.-D. Bierstedt, “Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I,” Journal für die Reine und Angewandte Mathematik, vol. 259, pp. 186–210, 1973. View at MathSciNet
  14. K.-D. Bierstedt, “Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. II,” Journal für die Reine und Angewandte Mathematik, vol. 260, pp. 133–146, 1973. View at Zentralblatt MATH · View at MathSciNet
  15. M. Fabian, P. Habala, P. Hájek, V. Montesinos, and V. Zizler, Banach Space Theory, Springer, New York, NY, USA, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. R. Meise and D. Vogt, Introduction to Functional Analysis, vol. 2 of Oxford Graduate Texts in Mathematics, The Clarendon Press Oxford University Press, New York, NY, USA, 1997, Translated from the German by M. S. Ramanujan and revised by the authors. View at MathSciNet
  17. P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland Mathematics Studies 131, Notas de Matemtica [Mathematical Notes] 113, North-Holland, Amsterdam, The Netherlands, 1987.
  18. S. Dineen, Complex Analysis on Infinite-Dimensional Spaces, Springer Monographs in Mathematics, Springer, London, UK, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  19. D. 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 Zentralblatt MATH · View at MathSciNet
  20. C. Boyd and S. Lassalle, “Geometry and analytic boundaries of Marcinkiewicz sequence spaces,” The Quarterly Journal of Mathematics, vol. 61, no. 2, pp. 183–197, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Globevnik, “On interpolation by analytic maps in infinite dimensions,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 83, no. 2, pp. 243–252, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. J. Globevnik, “Boundaries for polydisc algebras in infinite dimensions,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 85, no. 2, pp. 291–303, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. K. Seip, “Beurling type density theorems in the unit disk,” Inventiones Mathematicae, vol. 113, no. 1, pp. 21–39, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J. Bonet, P. Domański, and M. Lindström, “Weakly compact composition operators on analytic vector-valued function spaces,” Annales Academiæ Scientiarum Fennicæ, vol. 26, no. 1, pp. 233–248, 2001. View at Zentralblatt MATH · View at MathSciNet
  25. K. F. Ng, “On a theorem of Dixmier,” Mathematica Scandinavica, vol. 29, pp. 279–280, 1971. View at MathSciNet
  26. J. Horváth, Topological Vector Spaces and Distributions. Vol. I, Addison-Wesley, London, UK, 1966. View at MathSciNet
  27. G. Köthe, Topological Vector Spaces. II, vol. 237, Springer, Berlin, Germany, 1979. View at MathSciNet
  28. J. Bochnak and J. Siciak, “Polynomials and multilinear mappings in topological vector spaces,” Studia Mathematica, vol. 39, pp. 59–76, 1971. View at Zentralblatt MATH · View at MathSciNet
  29. B. Gramsch, “Ein Schwach-Stark-Prinzip der Dualitätstheorie lokalkonvexer Räume als Fortsetzungsmethode,” Mathematische Zeitschrift, vol. 156, no. 3, pp. 217–230, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. J. Bonet, M. C. Gómez-Collado, D. Jornet, and E. Wolf, “Operator-weighted composition operators between weighted spaces of vector-valued analytic functions,” Annales Academiæ Scientiarum Fennicæ, vol. 37, no. 2, pp. 319–338, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  31. K. 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 · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. K. D. Bierstedt and W. H. Summers, “Biduals of weighted Banach spaces of analytic functions,” Journal of the Australian Mathematical Society A, vol. 54, no. 1, pp. 70–79, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. J. Bonet and E. Wolf, “A note on weighted Banach spaces of holomorphic functions,” Archiv der Mathematik, vol. 81, no. 6, pp. 650–654, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. R. M. Aron and M. Schottenloher, “Compact holomorphic mappings on Banach spaces and the approximation property,” Bulletin of the American Mathematical Society, vol. 80, pp. 1245–1249, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. K. D. Bierstedt and S. Holtmanns, “Weak holomorphy and other weak properties,” Bulletin de la Société Royale des Sciences de Liège, vol. 72, no. 6, pp. 377–381, 2004. View at Zentralblatt MATH · View at MathSciNet