Banach Journal of Mathematical Analysis

The Gelfand--Phillips property in closed subspaces of some operator spaces

S. Mohammad Moshtaghioun and Manijeh Salimi

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By introducing the concept of limited completely continuous operators between two arbitrary Banach spaces $X$ and $Y$, we give some properties of this concept related to some well known classes of operators and specially, related to the Gelfand-Phillips property of the space $X$ or $Y$. Then some necessary and sufficient conditions for the Gelfand--Phillips property of closed subspace $M$ of some operator spaces, with respect to limited complete continuity of some operators on $M$, so-called, evaluation operators, are verified.

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Banach J. Math. Anal., Volume 5, Number 2 (2011), 84-92.

First available in Project Euclid: 14 August 2011

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Zentralblatt MATH identifier

Primary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]
Secondary: 47L20: Operator ideals [See also 47B10] 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]

Gelfand-Phillips property Schur property limited set evaluation operator operator ideal


Salimi, Manijeh; Moshtaghioun, S. Mohammad. The Gelfand--Phillips property in closed subspaces of some operator spaces. Banach J. Math. Anal. 5 (2011), no. 2, 84--92. doi:10.15352/bjma/1313363004.

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