On some subalgebras of and

Authors:
F. P. Cass and J. X. Gao

Journal:
Trans. Amer. Math. Soc. **347** (1995), 4461-4470

MSC:
Primary 47D30; Secondary 46B25, 46B28

MathSciNet review:
1311904

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Abstract | References | Similar Articles | Additional Information

Abstract: For a non-reflexive Banach space and , two families of subalgebras of , and for with for , were defined originally by Wilansky. We consider and and investigate relationships between the subalgebras for different . We prove in the case of that, for , all 's are isomorphic and all 's are isomorphic. For , where it is known that not all 's are isomorphic and not all 's are isomorphic, we show, surprisingly, that subalgebras associated with a Dirac measure on , regarded as a functional on , are isomorphic to those associated with some Banach limit (i.e., a translation invariant extended limit). We also obtain a representation for the operators in the subalgebras and of .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1995-1311904-2

Keywords:
Subalgebras,
operators on Banach spaces,
algebraic isomorphism,
Banach limits,
Dirac measures,
Stone-Čech compactification

Article copyright:
© Copyright 1995
American Mathematical Society