On compactness theorems for logarithmic interpolation methods



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Besoy, Blanca F. (2019) On compactness theorems for logarithmic interpolation methods. Banach Center Publications . ISSN 0137-6934 (Submitted)

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Let (A0;A1) be a Banach couple, (B0;B1) a quasi-Banach couple, 0 < q <= ∞ and T a linear operator. We prove that if T : A0 -> B0 is bounded and T : A1 -> B1 is compact, then the interpolated operator by the logarithmic method T : (A0,A1)1;q;A -> (B0;B1)1;q;A is compact too. This result allows the extension of some limit variants of Krasnosel'skii's compact interpolation theorem.

Item Type:Article
Uncontrolled Keywords:Logarithmic interpolation methods, compact operators, Lorentz-Zygmund spaces.
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:56936
Deposited On:11 Sep 2019 07:25
Last Modified:24 Sep 2019 09:33

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