Can one hear the structure of a Banach space? (Q1826098)
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scientific article; zbMATH DE number 4122681
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Can one hear the structure of a Banach space? |
scientific article; zbMATH DE number 4122681 |
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Can one hear the structure of a Banach space? (English)
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1989
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The author shows that the eigenvalues of any \(\gamma\)-summing (\(\ell\)- type) operator on a weak cotype-q-space belong to the weak \(\ell_ q\)- space \(\ell_{q,\infty}\) and that - as a partial converse - there exists a \(\gamma\)-summing operator on E whose eigenvalues do not belong to \(\ell_ q\) provided that E fails to be of weak cotype q. Some related problems are discussed.
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eigenvalues of any \(\gamma\)-summing operator
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\(\ell \)-type
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weak cotype- q-space
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