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Best possible Compactness Results of Lions-Peetre Type

Cobos, Fernando and Cwikel, M. and Matos, P. (2001) Best possible Compactness Results of Lions-Peetre Type. Proceedings of the Edinburgh Mathematical Society, 44 (Part 1). pp. 153-173. ISSN 0013-0915

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If T : A0 ! B boundedly and T : A1 ! B compactly, then a result of Lions{Peetre shows that T : A ! B compactly for a certain class of spaces A which are intermediate with respect to A0 and A1. We investigate to what extent such results can hold for arbitrary intermediate spaces A. The `dual' case of an operator S such that S : X ! Y0 boundedly and S : X ! Y1 compactly, is also considered,
as well as similar questions for other closed operator ideals.

Item Type:Article
Uncontrolled Keywords:Interpolation of Compact Operators; Rank-One Interpolation Spaces;General Intermediate Spaces; Operator Ideals; Mathematics
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15165

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