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The Schroeder-Bernstein property for Banach spaces. (English) Zbl 0684.46020
Banach space theory, Proc. Res. Workshop, Iowa City/Iowa 1987, Contemp. Math. 85, 61-77 (1989).
[For the entire collection see Zbl 0669.00012.]
A Banach space X is said to satisfy SBP (Schroeder-Bernstein property) if for any Banach space Y, if X and Y are isomorphic to complemented subspaces of one another, then X and Y are isomorphic.
First, the paper reviews spaces with SBP and then a list of spaces, for which SBP is unknown, is presented. Suitable techniques (e.g. Pelczynski’s decomposition method) are shown. Finally, likely candidates for counterexamples are examined.
Reviewer: Jerzy Szulga

MSC:
46B20 Geometry and structure of normed linear spaces