Interpolation of linear operators
نویسندگان
چکیده
منابع مشابه
Interpolation of Linear Operators
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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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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1956
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1956-0082586-0