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Lions–Schechter’s methods of complex interpolation and some quantitative estimates. (English) Zbl 1110.46015

After reviewing variants of the Lions–Schechter method of complex interpolation with derivatives, the author formulates some basic inequalities and then discusses the behaviour under Lions–Schechter interpolation of estimates for multidimensional rotundity of Banach spaces, measures of weak non-compactness, and spectral inequalities for bounded linear operators.

MSC:

46B70 Interpolation between normed linear spaces
46M35 Abstract interpolation of topological vector spaces
46A03 General theory of locally convex spaces
46B50 Compactness in Banach (or normed) spaces
47B07 Linear operators defined by compactness properties
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References:

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