The factorization property of ℓ^∞(X_k)

2019/10/22 by Lechner, R., Motakis, P., Müller, P. F. X. +1
#30H10 #46B25 #46B26 #47A68 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1910.11188

Abstract

In this paper we consider the following problem: Let X_k, be a Banach space with a normalized basis (e_(k,j))_j, whose biorthogonals are denoted by (e_(k,j)^*)_j, for k∈ℕ, let Z=ℓ^∞(X_k:k∈ℕ) be their ℓ^∞-sum, and let T:Z→ Z be a bounded linear operator, with a large diagonal, i.e. inf_k,j |e^*_(k,j)(T(e_(k,j))|gt;0. 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.

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