Twisted sums and a problem of Klee

DOI10.1007/BF02764838zbMATH Open0799.46085arXivmath/9302205MaRDI QIDQ1261901

N. Tenney Peck

Publication date: 7 September 1993

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Abstract: Let F be a quasi-linear map on a separable normed space X, and assume that F splits on an infinite-dimensional subspace of X. Then the twisted sum topology induced by F on the direct sum of X and the real line can be written as the supremum of a nearly convex topology and a trivial dual topology. (This partially answers a question of Klee.) The result applies when X is ell_1 and F is the Ribe function or when X is James's space.

Full work available at URL: https://arxiv.org/abs/math/9302205

zbMATH Keywords

twisted sumsproblem of Kleesupremum of a nearly convex topology and a trivial dual topology

Mathematics Subject Classification ID

Tensor products in functional analysis (46M05) Tensor products of linear operators (47A80)

Cites Work

• Uniformly Exhaustive Submeasures and Nearly Additive Set Functions
• Twisted Sums of Sequence Spaces and the Three Space Problem
• Examples for the Nonlocally Convex Three Space Problem
• Linear topologies which are suprema of dual-less topologies
• A Non-Reflexive Banach Space Isometric With Its Second Conjugate Space
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