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Operator Ideals Generalizing the Ideal of Strictly Singular Operators

✍ Scribed by Irmtraud Stephani

Publisher: John Wiley and Sons
Year: 1980
Tongue: English
Weight: 675 KB
Volume: 94
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19800940103

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✦ Synopsis

Abstract

It is well‐known that an operator T ∈ L(E, F) is strictly singular if ∥T~x~∥≧λ∥x∥ on a subspace Z ⊂ E implies dim Z < + ∞. The present paper deals with ideals of operators defined by a condition — ∥T~x~∥≧λ∥x∥ on an infinite‐dimensional subspace Z ⊂ E implies Z ∉ F — F being a „quasi‐injective”︁ class of BANACH spaces.

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