Characterizations of weakly K-analytic and Vasak spaces using projectional skeletons and separable PRI

Author(s)

Correa, Claudia ; Cuth, Marek ; Somaglia, Jacopo

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 515, n. 1, p. 25-pg., 2022-06-08.

Abstract

We find characterizations of Vasak spaces and weakly K-analytic spaces using the notions of separable projectional resolution of the identity (SPRI) and of projectional skeleton. This in particular addresses a recent challenge suggested by M. Fabian and V. Montesinos in [16]. Our method of proof also gives similar characterizations of WCG spaces and their subspaces (some aspects of which were known, some are new). Moreover we show that for countably many projectional skeletons {s(n) : n is an element of omega} on a Banach space inducing the same set, there exists a projectional skeleton on the space (indexed by ranges of the corresponding projections) which is isomorphic to a subskeleton of each s(n), n is an element of omega. (C) 2022 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/09797-2 - Geometry of C(K)-Banach spaces
• Grantee: Claudia Correa de Andrade Oliveira
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/08515-6 - Generalizations of Sobczyk's Theorem for C(K) Banach spaces
• Grantee: Claudia Correa de Andrade Oliveira
• Support Opportunities: Scholarships abroad - Research