Banach spaces for which the space of operators has 2c closed ideals
Forum of Mathematics, Sigma, Tome 9 (2021)
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We formulate general conditions which imply that ${\mathcal L}(X,Y)$, the space of operators from a Banach space X to a Banach space Y, has $2^{{\mathfrak {c}}}$ closed ideals, where ${\mathfrak {c}}$ is the cardinality of the continuum. These results are applied to classical sequence spaces and Tsirelson-type spaces. In particular, we prove that the cardinality of the set ofclosed ideals in ${\mathcal L}\left (\ell _p\oplus \ell _q\right )$ is exactly $2^{{\mathfrak {c}}}$ for all $1$.
@article{10_1017_fms_2021_23,
author = {Daniel Freeman and Thomas Schlumprecht and Andr\'as Zs\'ak},
title = {Banach spaces for which the space of operators has 2c closed ideals},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {9},
year = {2021},
doi = {10.1017/fms.2021.23},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.23/}
}
TY - JOUR AU - Daniel Freeman AU - Thomas Schlumprecht AU - András Zsák TI - Banach spaces for which the space of operators has 2c closed ideals JO - Forum of Mathematics, Sigma PY - 2021 VL - 9 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.23/ DO - 10.1017/fms.2021.23 LA - en ID - 10_1017_fms_2021_23 ER -
%0 Journal Article %A Daniel Freeman %A Thomas Schlumprecht %A András Zsák %T Banach spaces for which the space of operators has 2c closed ideals %J Forum of Mathematics, Sigma %D 2021 %V 9 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.23/ %R 10.1017/fms.2021.23 %G en %F 10_1017_fms_2021_23
Daniel Freeman; Thomas Schlumprecht; András Zsák. Banach spaces for which the space of operators has 2c closed ideals. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2021.23
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