On the complexity of some classes of Banach spaces and non-universality

Title:

On the complexity of some classes of Banach spaces and non-universality

Creator:

Bruno M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:edc732a9-00f4-4f5d-9393-13abaf382d26
uuid:edc732a9-00f4-4f5d-9393-13abaf382d26

Subject:

Banach-Saks operator, Dunford-Pettis property, analytic Radon-Nikodym property, complete continuous property, Schur property, unconditionally converging operator, weakly compact operator, local structure, non-universality, $\ell _p$-Baire sum, descriptive set theory, and tree

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the LUST property. We also show that the weak Banach-Saks property, the Schur property, the Dunford-Pettis property, the analytic Radon-Nikodym property, the set of Banach spaces whose set of unconditionally converging operators is complemented in its bounded operators, the set of Banach spaces whose set of weakly compact operators is complemented in its bounded operators, and the set of Banach spaces whose set of Banach-Saks operators is complemented in its bounded operators, are all non Borel in ${\rm SB}$. At last, we give several applications of those results to non-universality results.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1123-1147

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:4

Harvested from:

CDK

Metadata only:

false