Uncomplementability of spaces of compact operators in larger spaces of operators

Giovanni Emmanuele; Kamil John

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 1, page 19-32
  • ISSN: 0011-4642

Abstract

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In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of c 0 in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results in the paper.

How to cite

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Emmanuele, Giovanni, and John, Kamil. "Uncomplementability of spaces of compact operators in larger spaces of operators." Czechoslovak Mathematical Journal 47.1 (1997): 19-32. <http://eudml.org/doc/30344>.

@article{Emmanuele1997,
abstract = {In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of $c_0$ in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results in the paper.},
author = {Emmanuele, Giovanni, John, Kamil},
journal = {Czechoslovak Mathematical Journal},
keywords = {spaces of linear and compact operators; non existence of projections; copies of $c_0$; Approximation properties; non existence of norm one projection; Hahn-Banach extensions; spaces of linear and compact operators; non existence of projections; copies of ; approximation properties; non existence of norm one projection; Hahn-Banach extensions},
language = {eng},
number = {1},
pages = {19-32},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uncomplementability of spaces of compact operators in larger spaces of operators},
url = {http://eudml.org/doc/30344},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Emmanuele, Giovanni
AU - John, Kamil
TI - Uncomplementability of spaces of compact operators in larger spaces of operators
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 1
SP - 19
EP - 32
AB - In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of $c_0$ in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results in the paper.
LA - eng
KW - spaces of linear and compact operators; non existence of projections; copies of $c_0$; Approximation properties; non existence of norm one projection; Hahn-Banach extensions; spaces of linear and compact operators; non existence of projections; copies of ; approximation properties; non existence of norm one projection; Hahn-Banach extensions
UR - http://eudml.org/doc/30344
ER -

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Citations in EuDML Documents

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  1. Kamil John, Projections from L ( X , Y ) onto K ( X , Y )
  2. Ioana Ghenciu, A note on Dunford-Pettis like properties and complemented spaces of operators
  3. Ioana Ghenciu, The reciprocal Dunford–Pettis property of order p in projective tensor products
  4. Giovanni Emmanuele, On the position of the space of representable operators in the space of linear operators 1
  5. Ioana Ghenciu, Property ( 𝐰𝐋 ) and the reciprocal Dunford-Pettis property in projective tensor products

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