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)

 

 

Functions operating from a complex Banach space to its real part


Author: Eggert Briem
Journal: Proc. Amer. Math. Soc. 125 (1997), 861-867
MSC (1991): Primary 46E15, 46J10
MathSciNet review: 1363450
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider functions operating from a complex Banach function space to its real part. We show among other things, that if $|b|\in {\rm Re}B$ for all $b$ in an ultraseparating Banach function space $B$, then Re$B=C_ { \mathbf {R}}(X)$.


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

  • 1. A. Bernard, Espace des parties réelles des éléments d’une algèbre de Banach de fonctions, J. Functional Analysis 10 (1972), 387–409 (French, with English summary). MR 0343037
  • 2. Alain Bernard, Une fonction non lipschitzienne peut-elle opérer sur un espace de Banach de fonctions non trivial?, J. Funct. Anal. 122 (1994), no. 2, 451–477 (French, with English and French summaries). MR 1276166, 10.1006/jfan.1994.1076
  • 3. Eggert Briem, Operating functions and ultraseparating function spaces, Function spaces (Edwardsville, IL, 1990) Lecture Notes in Pure and Appl. Math., vol. 136, Dekker, New York, 1992, pp. 55–59. MR 1152336
  • 4. E. Briem and K. Jarosz, Operating functions for Banach function spaces, to appear in the Rocky Mount. J. of Math.
  • 5. O. Hatori, Range transformations on a Banach function algebra III, Kitasato J. Liberal Arts and Sciences 23 (1989), 78-84.
  • 6. Osamu Hatori, Separation properties and operating functions on a space of continuous functions, Internat. J. Math. 4 (1993), no. 4, 551–600. MR 1232985, 10.1142/S0129167X93000303
  • 7. Karel de Leeuw and Yitzhak Katznelson, Functions that operate on non-self-adjoint algebras, J. Analyse Math. 11 (1963), 207–219. MR 0158282
  • 8. S. J. Sidney, Functions which operate on the real part of a uniform algebra, Pacific J. Math. 80 (1979), no. 1, 265–272. MR 534716

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46E15, 46J10

Retrieve articles in all journals with MSC (1991): 46E15, 46J10


Additional Information

Eggert Briem
Affiliation: Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland
Email: briem@rhi.hi.is

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03655-1
Keywords: Operating functions, function space, ultraseparation
Received by editor(s): March 9, 1995
Received by editor(s) in revised form: October 4, 1995
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society