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

0558320 - MÚ 2023 RIV US eng J - Článek v odborném periodiku
Correa, C. - Cúth, Marek - Somaglia, J.
Characterizations of weakly K-analytic and Vašák spaces using projectional skeletons and separable PRI.
Journal of Mathematical Analysis and Applications. Roč. 515, č. 1 (2022), č. článku 126389. ISSN 0022-247X. E-ISSN 1096-0813
Grant CEP: GA ČR(CZ) GJ19-05271Y
Institucionální podpora: RVO:67985840
Klíčová slova: method of suitable models * projectional skeleton * separable projectional resolution of the identity * Vašák space
Obor OECD: Pure mathematics
Impakt faktor: 1.3, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jmaa.2022.126389

We find characterizations of Vašák 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 {sn:n∈ω} 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 sn, n∈ω.
Trvalý link: http://hdl.handle.net/11104/0332046