An approximation property related to -ideals of compact operators

Authors:
Rafael Payá and Wend Werner

Journal:
Proc. Amer. Math. Soc. **111** (1991), 993-1001

MSC:
Primary 46B20; Secondary 47B07, 47D15, 47D30

MathSciNet review:
1039261

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Abstract: We investigate a variant of the compact metric approximation property which, for subspaces of , is known to be equivalent to , the space of compact operators on , being an -ideal in the space of bounded operators on . Among other things, it is shown that an arbitrary Banach space has this property iff is an -ideal in for all Banach spaces and, furthermore, that must contain a copy of . The proof of the central theorem of this note uses a characterization of those Banach spaces for which is an -ideal in obtained earlier by the second author, as well as some techniques from Banach algebra theory.

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1039261-1

Article copyright:
© Copyright 1991
American Mathematical Society