The factorisation property of l∞(Xk)
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Abstract In this paper we consider the following problem: let Xk, 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.
1997 ◽
Vol 56
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pp. 303-318
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1981 ◽
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pp. 77-81
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1986 ◽
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pp. 65-86
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1987 ◽
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pp. 1223-1234
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1970 ◽
Vol 22
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1989 ◽
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pp. 456-468
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1991 ◽
Vol 14
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pp. 611-614
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