Small operator ideals on the Schlumprecht and Schreier spaces

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<p<q<\infty $ .

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Small operator ideals on the Schlumprecht and Schreier spaces

Cited by 2 publications

References 23 publications

Equivalence of block sequences in Schreier spaces and their duals

Equivalence of block sequences in Schreier spaces and their duals

Banach spaces for which the space of operators has 2^𝔠closed ideals

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Small operator ideals on the Schlumprecht and Schreier spaces

Cited by 2 publications

References 23 publications

Equivalence of block sequences in Schreier spaces and their duals

Equivalence of block sequences in Schreier spaces and their duals

Banach spaces for which the space of operators has 2𝔠closed ideals

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Product

Resources

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Banach spaces for which the space of operators has 2^𝔠closed ideals