-ideals of compact operators

are separably determined

Author:
Eve Oja

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2747-2753

MSC (1991):
Primary 46B28, 47D15, 46B20

MathSciNet review:
1469429

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the space of compact operators on a Banach space is an -ideal in the space of bounded operators if and only if has the metric compact approximation property (MCAP), and is an -ideal in for all separable subspaces of having the MCAP. It follows that the Kalton-Werner theorem characterizing -ideals of compact operators on separable Banach spaces is also valid for non-separable spaces: for a Banach space is an -ideal in if and only if has the MCAP, contains no subspace isomorphic to and has property It also follows that is an -ideal in for all Banach spaces if and only if has the MCAP, and is an -ideal in .

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Additional Information

**Eve Oja**

Affiliation:
Institute of Pure Mathematics, Tartu University, Vanemuise 46, EE2400 Tartu, Estonia

Email:
eveoja@math.ut.ee

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04600-0

Received by editor(s):
February 14, 1997

Additional Notes:
The author was partially supported by the Estonian Science Foundation Grant 3055.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society