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The factorisation property of l∞(Xk).
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Sep2021, Vol. 171 Issue 2, p421-448. 28p. - Publication Year :
- 2021
-
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 ∈ N, let Z = ℓ∞(Xk : k ∈ N) be their l∞-sum, and let T : Z → Z be a bounded linear operator with a large diagonal, i.e., infk,j|e*(k,j)(T(e(k,j))| > 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BANACH spaces
Subjects
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 171
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 151873079
- Full Text :
- https://doi.org/10.1017/S0305004120000304