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A note on extensions of Pełczyński’s decomposition method in Banach spaces. (English) Zbl 1128.46006

This paper extends a series giving variations of Pełczyński’s decomposition method. This one completely characterizes those sextuples \((p,q,r,s,u,v)\) of natural numbers such that, for arbitrary Banach spaces \(X,Y,A,B\), the hypotheses \(X\sim Y\oplus A\), \(Y\sim X\oplus B\), \(X^u\sim X^p \oplus Y^q\) and \(Y^v\sim A^r\oplus B^s\) guarantee that \(X\sim Y\).

MSC:

46B03 Isomorphic theory (including renorming) of Banach spaces
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