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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 78928, 13 pages
http://dx.doi.org/10.1155/AAA/2006/78928

Bourgin-Yang-type theorem for a-compact perturbations of closed operators. Part I. The case of index theories with dimension property

1Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, México DF 04510, Mexico
2Department of Mathematics and Computer Science, Netanya Academic College, Netanya 42365, Israel
3Faculty of Mathematics, Voronezh State University, 1 Universitetskaya Pl., Voronezh 394006, Russia

Received 26 June 2005; Accepted 1 July 2005

Copyright © 2006 Sergey A. Antonyan et al. 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. S. A. Antonyan, “Retracts in categories of G-spaces,” Izvestiya Akademii Nauk Armyanskoĭ SSR. Seriya Matematika, vol. 15, no. 5, pp. 365–378, 1980, English translation in: Soviet Journal of Contemporary Mathematical Analysis \textbf{15} (1980), 30–43. View at Zentralblatt MATH · View at MathSciNet
  2. J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons, New York, 1984. View at Zentralblatt MATH · View at MathSciNet
  3. T. Bartsch, Topological Methods for Variational Problems with Symmetries, vol. 1560 of Lecture Notes in Mathematics, Springer, Berlin, 1993. View at Zentralblatt MATH · View at MathSciNet
  4. V. Benci, “On critical point theory for indefinite functionals in the presence of symmetries,” Transactions of the American Mathematical Society, vol. 274, no. 2, pp. 533–572, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. G. Bourgin, “On some separation and mapping theorems,” Commentarii Mathematici Helvetici, vol. 29, pp. 199–214, 1955. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York, 1972. View at MathSciNet
  7. Z. Dzedzej, “Equivariant selections and approximations,” in Topological Methods in Nonlinear Analysis, pp. 25–31, Gdansk Scientific Society, Gdansk, 1997.
  8. B. D. Gel'man, “The Borsuk-Ulam theorem in infinite-dimensional Banach spaces,” Sbornik: Mathematics, vol. 193, no. 1, pp. 83–91, 2002. View at Zentralblatt MATH · View at MathSciNet
  9. B. D. Gel'man, “An infinite-dimensional version of the Borsuk-Ulam theorem,” Functional Analysis and Its Applications, vol. 38, no. 4, pp. 1–5, 2004. View at Zentralblatt MATH · View at MathSciNet
  10. P. Holm and E. H. Spanier, “Involutions and Fredholm maps,” Topology, vol. 10, no. 3, pp. 203–218, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Ize and A. Vignoli, Equivariant Degree Theory, vol. 8 of De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 2003. View at Zentralblatt MATH · View at MathSciNet
  12. W. Krawcewicz and J. Wu, Theory of Degrees with Applications to Bifurcations and Differential Equations, John Wiley & Sons, New York, 1997. View at Zentralblatt MATH · View at MathSciNet
  13. A. Kushkuley and Z. I. Balanov, Geometric Methods in Degree Theory for Equivariant Maps, vol. 1632 of Lecture Notes in Mathematics, Springer, Berlin, 1996. View at Zentralblatt MATH · View at MathSciNet
  14. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74 of Applied Mathematical Sciences, Springer, New York, 1989. View at Zentralblatt MATH · View at MathSciNet
  15. E. Michael, “Continuous selections I,” Annals of Mathematics, vol. 63, pp. 361–382, 1956. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. W. Rudin, Functional Analysis, McGraw-Hill, New York, 2nd edition, 1991. View at Zentralblatt MATH · View at MathSciNet
  17. H. Steinlein, “Borsuk's antipodal theorem and its generalizations and applications: a survey,” in Topological Methods in Nonlinear Analysis, A. Granas, Ed., vol. 95 of Sém Mathematics Sup., pp. 166–235, Presses de l ' Université of Montréal, Montreal, 1985. View at Zentralblatt MATH · View at MathSciNet
  18. I. A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967. View at Zentralblatt MATH · View at MathSciNet
  19. C.-T. Yang, “On theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobo and Dyson I,” Annals of Mathematics, vol. 60, pp. 262–282, 1954. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. D. P. Zhelobenko, Introduction to Representation Theory, Factorial Press, Moscow, 2001.
  21. D. P. Zhelobenko and A. I. Shtern, Representations of Lie Groups, Nauka, Moscow, 1983. View at Zentralblatt MATH · View at MathSciNet