A note on Dunford-Pettis like properties and complemented spaces of operators

Ioana Ghenciu

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 2, page 207-222
  • ISSN: 0010-2628

Abstract

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Equivalent formulations of the Dunford-Pettis property of order p ( D P P p ), 1 < p < ∞ , are studied. Let L ( X , Y ) , W ( X , Y ) , K ( X , Y ) , U ( X , Y ) , and C p ( X , Y ) denote respectively the sets of all bounded linear, weakly compact, compact, unconditionally converging, and p -convergent operators from X to Y . Classical results of Kalton are used to study the complementability of the spaces W ( X , Y ) and K ( X , Y ) in the space C p ( X , Y ) , and of C p ( X , Y ) in U ( X , Y ) and L ( X , Y ) .

How to cite

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Ghenciu, Ioana. "A note on Dunford-Pettis like properties and complemented spaces of operators." Commentationes Mathematicae Universitatis Carolinae 59.2 (2018): 207-222. <http://eudml.org/doc/294799>.

@article{Ghenciu2018,
abstract = {Equivalent formulations of the Dunford-Pettis property of order $p$ ($\{DPP\}_p$), $1<p<\infty $, are studied. Let $L(X,Y)$, $W(X,Y)$, $K(X,Y)$, $U(X,Y)$, and $C_p(X,Y)$ denote respectively the sets of all bounded linear, weakly compact, compact, unconditionally converging, and $p$-convergent operators from $X$ to $Y$. Classical results of Kalton are used to study the complementability of the spaces $W(X,Y)$ and $K(X,Y)$ in the space $C_p(X,Y)$, and of $C_p(X,Y)$ in $U(X,Y)$ and $L(X,Y)$.},
author = {Ghenciu, Ioana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Dunford-Pettis property of order $p$; $p$-convergent operator; complemented spaces of operators},
language = {eng},
number = {2},
pages = {207-222},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on Dunford-Pettis like properties and complemented spaces of operators},
url = {http://eudml.org/doc/294799},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Ghenciu, Ioana
TI - A note on Dunford-Pettis like properties and complemented spaces of operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 2
SP - 207
EP - 222
AB - Equivalent formulations of the Dunford-Pettis property of order $p$ (${DPP}_p$), $1<p<\infty $, are studied. Let $L(X,Y)$, $W(X,Y)$, $K(X,Y)$, $U(X,Y)$, and $C_p(X,Y)$ denote respectively the sets of all bounded linear, weakly compact, compact, unconditionally converging, and $p$-convergent operators from $X$ to $Y$. Classical results of Kalton are used to study the complementability of the spaces $W(X,Y)$ and $K(X,Y)$ in the space $C_p(X,Y)$, and of $C_p(X,Y)$ in $U(X,Y)$ and $L(X,Y)$.
LA - eng
KW - Dunford-Pettis property of order $p$; $p$-convergent operator; complemented spaces of operators
UR - http://eudml.org/doc/294799
ER -

References

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