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

Bruno M. Braga

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 4, page 1123-1147
  • ISSN: 0011-4642

Abstract

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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 SB . At last, we give several applications of those results to non-universality results.

How to cite

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Braga, Bruno M.. "On the complexity of some classes of Banach spaces and non-universality." Czechoslovak Mathematical Journal 64.4 (2014): 1123-1147. <http://eudml.org/doc/269847>.

@article{Braga2014,
abstract = {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.},
author = {Braga, Bruno M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {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; tree; 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; tree},
language = {eng},
number = {4},
pages = {1123-1147},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the complexity of some classes of Banach spaces and non-universality},
url = {http://eudml.org/doc/269847},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Braga, Bruno M.
TI - On the complexity of some classes of Banach spaces and non-universality
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 1123
EP - 1147
AB - 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.
LA - eng
KW - 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; tree; 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; tree
UR - http://eudml.org/doc/269847
ER -

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