Unconditional ideals of finite rank operators

Trond A. Abrahamsen; Asvald Lima; Vegard Lima

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 1257-1278
  • ISSN: 0011-4642

Abstract

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Let X be a Banach space. We give characterizations of when ℱ ( Y , X ) is a u -ideal in 𝒲 ( Y , X ) for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when ℱ ( X , Y ) is a u -ideal in 𝒲 ( X , Y ) for every Banach space Y , when ℱ ( Y , X ) is a u -ideal in 𝒲 ( Y , X * * ) for every Banach space Y , and when ℱ ( Y , X ) is a u -ideal in 𝒦 ( Y , X * * ) for every Banach space Y .

How to cite

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Abrahamsen, Trond A., Lima, Asvald, and Lima, Vegard. "Unconditional ideals of finite rank operators." Czechoslovak Mathematical Journal 58.4 (2008): 1257-1278. <http://eudml.org/doc/37902>.

@article{Abrahamsen2008,
abstract = {Let $X$ be a Banach space. We give characterizations of when $\{\mathcal \{F\}\}(Y,X)$ is a $u$-ideal in $\{\mathcal \{W\}\}(Y,X)$ for every Banach space $Y$ in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when $\{\mathcal \{F\}\}(X,Y)$ is a $u$-ideal in $\{\mathcal \{W\}\}(X,Y)$ for every Banach space $Y$, when $\{\mathcal \{F\}\}(Y,X)$ is a $u$-ideal in $\{\mathcal \{W\}\}(Y,X^\{**\})$ for every Banach space $Y$, and when $\{\mathcal \{F\}\}(Y,X)$ is a $u$-ideal in $\{\mathcal \{K\}\}(Y,X^\{**\})$ for every Banach space $Y$.},
author = {Abrahamsen, Trond A., Lima, Asvald, Lima, Vegard},
journal = {Czechoslovak Mathematical Journal},
keywords = {$u$-ideals; finite rank; compact; and weakly compact operators; Hahn-Banach extension operators; -ideal; finite rank operator; Hahn-Banach extension operator},
language = {eng},
number = {4},
pages = {1257-1278},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unconditional ideals of finite rank operators},
url = {http://eudml.org/doc/37902},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Abrahamsen, Trond A.
AU - Lima, Asvald
AU - Lima, Vegard
TI - Unconditional ideals of finite rank operators
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1257
EP - 1278
AB - Let $X$ be a Banach space. We give characterizations of when ${\mathcal {F}}(Y,X)$ is a $u$-ideal in ${\mathcal {W}}(Y,X)$ for every Banach space $Y$ in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when ${\mathcal {F}}(X,Y)$ is a $u$-ideal in ${\mathcal {W}}(X,Y)$ for every Banach space $Y$, when ${\mathcal {F}}(Y,X)$ is a $u$-ideal in ${\mathcal {W}}(Y,X^{**})$ for every Banach space $Y$, and when ${\mathcal {F}}(Y,X)$ is a $u$-ideal in ${\mathcal {K}}(Y,X^{**})$ for every Banach space $Y$.
LA - eng
KW - $u$-ideals; finite rank; compact; and weakly compact operators; Hahn-Banach extension operators; -ideal; finite rank operator; Hahn-Banach extension operator
UR - http://eudml.org/doc/37902
ER -

References

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