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Some Compactness Results in Real Interpolation for Families of Banach Spaces
Author(s) -
Carro María J.,
Peetre Jaak
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610796006515
Subject(s) - mathematics , compact space , banach space , pure mathematics , functor , interpolation (computer graphics) , interpolation space , compact operator , discrete mathematics , functional analysis , image (mathematics) , extension (predicate logic) , computer science , biochemistry , chemistry , artificial intelligence , gene , programming language
The paper shows that, if the operator T : A (γ)→ B (γ) is compact for almost every γ∈Γ, then T : F ( A ¯ ) → F ( B ¯ )is compact when F ( X ¯ ) =( X ) K Sor F ( X ¯ ) =( X ) J Sis the interpolation functor constructed for infinite families of Banach spaces and S satisfies certain conditions.