One-Sided Compactness Results for Aronszajn-Gagliardo Functors



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Cobos, Fernando and Kühn, Thomas and Schonbek, T. (1992) One-Sided Compactness Results for Aronszajn-Gagliardo Functors. Journal of Functional Analysis , 106 (2). pp. 274-313. ISSN 0022-1236

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Interpolating compactness properties of operators is a long standing and important problem. In this paper, the authors consider the problem in a very general setting of Aronszajn-Gagliardo functors. In simplest terms they show that if T : A0 ! B0 is compact and T : A1 ! B1 is bounded, then T is compact on some interpolation spaces constructed in the Aronszajn-Gagliardo methods. These methods do not include the complex interpolation method, but the authors show that if the two couples are formed by Banach lattices then the theorem holds in the complex method as well. Additional results are in the context of interpolation of compactness properties in the context of N-tuples of Banach spaces. The paper includes a number of related, interesting results.

Item Type:Article
Uncontrolled Keywords:Interpolating compactness properties of operators; Aronszajn-Gagliardo functors; Banach lattices
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15494
Deposited On:06 Jun 2012 07:49
Last Modified:25 Oct 2013 14:15

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