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M-Ideals in L(l1, E)

Published online by Cambridge University Press:  20 November 2018

D. J. Fleming and
D. M. Giarrusso
D. J. Fleming
Affiliation:
Department of Mathematics, St. Lawrence University Canton, NY 13617, U.S.A.
D. M. Giarrusso
Affiliation:
Department of Mathematics, St. Lawrence University Canton, NY 13617, U.S.A.
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Abstract

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In this article it is shown that for any Banach space E,L (l1,E) always contains uncountably many distinct A/-ideals that are closed subspaces of K(l1,E) and which are not complemented in L (l1,E) . Using standard duality arguments one obtains the result that infinitely many distinct subspaces of K(E, c0) are M-ideals in L(E, c0). In particular, for the case E = c0, this shows that the uniqueness conditions enjoyed by K(lp), p > 1, is not valid for E = c0. The results are obtained by utilizing the identification of L (l1,E) with the vector-valued sequence space lx(E) and to exploit natural decompositions of lx(E)’ afforded by a class of Lprojections on lx(E)’ induced by certain E'-valued vector measures.

Keywords

Primary 46B20Secondary 46A32

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986, pp. 3 - 10
Copyright
Copyright © Canadian Mathematical Society 1986

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