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Title: The factorisation property of l ∞ ( Xk )
Abstract In this paper we consider the following problem: let X k , be a Banach space with a normalised basis ( e (k, j) ) j , whose biorthogonals are denoted by ${(e_{(k,j)}^*)_j}$ , for $k\in\N$ , let $Z=\ell^\infty(X_k:k\kin\N)$ be their l ∞ -sum, and let $T:Z\to Z$ be a bounded linear operator with a large diagonal, i.e. , $$\begin{align*}\inf_{k,j} \big|e^*_{(k,j)}(T(e_{(k,j)})\big|>0.\end{align*}$$ Under which condition does the identity on Z factor through T ? The purpose of this paper is to formulate general conditions for which the answer is positive.  more » « less
Award ID(s):
1764343
PAR ID:
10337517
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Mathematical Proceedings of the Cambridge Philosophical Society
Volume:
171
Issue:
2
ISSN:
0305-0041
Page Range / eLocation ID:
421 to 448
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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