Real interpolation and compact linear operators
نویسندگان
چکیده
منابع مشابه
Complex Interpolation of Compact Operators
If (A0, A1) and (B0, B1) are Banach couples and a linear operator T : A0 +A1 → B0 +B1 maps A0 compactly into B0 and maps A1 boundedly into B1, does T necessarily also map [A0, A1]θ compactly into [B0, B1]θ for θ ∈ (0, 1)? After 42 years this question is still not answered, not even in the case where T : A1 → B1 is also compact. But affirmative answers are known for many special choices of (A0, ...
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The aim of this paper is to prove a generalization of a well-known convexity theorem of M. Riesz [8]. The Riesz theorem was originally deduced by "real-variable" techniques. Later, Thorin [10], Tamarkin and Zygmund [9], and Thorin [ll] introduced convexity properties of analytic functions in their study of Riesz's theorem. These ideas were put in especially suggestive form by A. P. Calderon and...
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After 41 years it is still not known whether an operator acting on a Banach pair and which acts compactly on one or both of the “endpoint” spaces also acts compactly on the complex interpolation spaces generated by the pair. We report some recent steps towards solving this and related problems.
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This thesis deals with linear ill-posed problems related to compact operators, and iterative Krylov subspace methods for solving discretized versions of these. Linear compact operators in infinite dimensional Hilbert spaces will be investigated and several results on the singular values and eigenvalues for such will be presented. A large subset of linear compact operators consists of integral o...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1990
ISSN: 0022-1236
DOI: 10.1016/0022-1236(90)90110-7