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On Some Classes of Primary Banach Spaces

Published online by Cambridge University Press:  20 November 2018

P. G. Casazza ,
C. A. Kottman  and
Bor-Luh Lin
P. G. Casazza
Affiliation:
The University of Alabama in Huntsville, Huntsville, Alabama
C. A. Kottman
Affiliation:
Oregon State University, Corvallis, Oregon
Bor-Luh Lin
Affiliation:
The University of Iowa, Iowa City, Iowa
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A Banach space X is called primary (respectively, prime) if for every (bounded linear) projection P on X either PX or (I — P)X (respectively, PX with dim PX = ∞ ) is isomorphic to X. It is well-known that C0 and lp, 1 ≦ p ≦ ∞ [8; 14] are prime. However, it is unknown whether there are other prime Banach spaces. For a discussion on prime and primary Banach spaces, we refer the reader to [9].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 856 - 873
Copyright
Copyright © Canadian Mathematical Society 1977

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