Isomorphisms of standard operator algebras

Author:
Peter Šemrl

Journal:
Proc. Amer. Math. Soc. **123** (1995), 1851-1855

MSC:
Primary 47D30

DOI:
https://doi.org/10.1090/S0002-9939-1995-1242104-8

MathSciNet review:
1242104

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Abstract: Let *X* and *Y* be Banach spaces, , and let and be standard operator algebras on *X* and *Y*, respectively. Assume that is a bijective mapping satisfying , where is a given positive real number (no linearity or continuity of is assumed). Then is a spatially implemented linear or conjugate linear algebra isomorphism. In particular, is continuous.

**[1]**J. Aczél and J. Dhombres,*Functional equations in several variables*, Encyclopedia Math. Appl., vol. 31, Cambridge Univ. Press, Cambridge, 1989. MR**1004465 (90h:39001)****[2]**J. A. Baker,*The stability of the cosine equation*, Proc. Amer. Math. Soc.**80**(1980), 411-416. MR**580995 (81m:39015)****[3]**D. G. Bourgin,*Approximately isometric and multiplicative transformations on continuous function rings*, Duke Math. J.**16**(1949), 385-397. MR**0031194 (11:115e)****[4]**P. R. Chernoff,*Representations, automorphisms, and derivations of some operator algebras*, J. Funct. Anal.**12**(1973), 275-289. MR**0350442 (50:2934)****[5]**D. H. Hyers,*The stability of homomorphisms and related topics*, Global Analysis--Analysis on Manifolds (Th. M. Rassias, ed.), Teubner-Texte Math., Teubner, Leipzig, 1983, pp. 140-153. MR**730609 (86a:39004)****[6]**I. Kaplansky,*Ring isomorphisms of Banach algebras*, Canad. J. Math.**6**(1954), 374-381. MR**0062960 (16:49e)****[7]**-,*Algebraic and analytic aspects of operator algebras*, CBMS Regional Conf. Ser. in Math., Amer. Math. Soc., Providence, RI, 1970. MR**0312283 (47:845)****[8]**W. S. Martindale III,*When are multiplicative mappings additive*?, Proc. Amer. Math. Soc.**21**(1969), 695-698. MR**0240129 (39:1483)****[9]**C. E. Rickart,*Representations of certain Banach algebras on Hilbert space*, Duke Math. J.**18**(1951), 27-39. MR**0050807 (14:385f)**

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1242104-8

Article copyright:
© Copyright 1995
American Mathematical Society