Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Canonical mappings for polynomials and holomorphic functions on Banach spaces

Author: Seán Dineen
Journal: Proc. Amer. Math. Soc. 129 (2001), 2897-2905
MSC (2000): Primary 46G20; Secondary 46G25
Published electronically: March 15, 2001
MathSciNet review: 1840091
Full-text PDF

Abstract | References | Similar Articles | Additional Information


We obtain functional representations for the canonical mapping into the bidual for spaces of holomorphic functions on certain Banach spaces.

References [Enhancements On Off] (What's this?)

  • 1. R. Alencar, R. M. Aron, S. Dineen, A reflexive space of holomorphic functions in infinitely many variables, Proc. Amer. Math. Soc., 90, 1984, 407-411. MR 85b:46050
  • 2. R. M. Aron, S. Dineen, $Q$-reflexive Banach spaces, Rocky Mountain J. Math., 27, 4, 1997, 1009-1025. MR 99h:46010
  • 3. C. Boyd, R. A. Ryan, Geometric theory of spaces of integral polynomials and symmetric tensor products, J. Funct. Anal., (to appear).
  • 4. D. Carando, V. Dimant, Duality in spaces of nuclear and integral polynomials, J. Math. Ann. Appl. 241, 2000, 107-121. CMP 2000:07
  • 5. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Monographs in Mathematics, Springer Verlag (1999). CMP 99:17
  • 6. P. Galindo, M. Maestre, P. Rueda, Biduality in spaces of holomorphic functions, Math. Scand., 86, 2000, 5-16. CMP 2000:07
  • 7. M. González, Remarks on $Q$-reflexive spaces, Proc. Royal Irish Acad. Sect. A, 96, 2, 1996, 195-201. MR 99f:46024
  • 8. J. Horváth, Topological Vector Spaces and Distributions, Vol. I, Addison-Wesley, Reading, Massachusetts, 1996. MR 34:4863
  • 9. J. Mujica, M. Valdivia, Holomorphic germs on Tsirelson's space, Proc. Amer. Math. Soc.,123, 5, 1995, 1379-1386. MR 95f:46074
  • 10. L. Nachbin, Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci. U.S.A., 40, 1954, 471-474. MR 16:156h
  • 11. T. Shirota, On locally convex vector spaces of continuous functions, Proc. Japan Acad. Ser. A, Math.Sci. 30, 1954, 294-298. MR 16:1030d

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46G20, 46G25

Retrieve articles in all journals with MSC (2000): 46G20, 46G25

Additional Information

Seán Dineen
Affiliation: Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland

Received by editor(s): January 6, 1999
Received by editor(s) in revised form: February 2, 2000
Published electronically: March 15, 2001
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society