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Complex interpolation functors with a family of quasi-power function parameters. (English) Zbl 0805.46075

Summary: For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskij construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters which are quasi-powers with a logarithmic factor.

MSC:

46M35 Abstract interpolation of topological vector spaces
46B70 Interpolation between normed linear spaces
46M15 Categories, functors in functional analysis
46B03 Isomorphic theory (including renorming) of Banach spaces
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