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Abstract limit J ‐spaces
Author(s) -
Cobos Fernando,
Fernández-Cabrera Luz M.,
Mastyło Mieczysław
Publication year - 2010
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/jlms/jdq043
Subject(s) - interpolation space , mathematics , birnbaum–orlicz space , function space , pure mathematics , limit (mathematics) , sequence (biology) , compact open topology , interpolation (computer graphics) , limit of a sequence , banach space , uniform limit theorem , invariant (physics) , topological tensor product , fréchet space , compact space , lp space , inverse limit , functional analysis , mathematical analysis , computer science , animation , biochemistry , chemistry , genetics , computer graphics (images) , biology , mathematical physics , gene
We investigate the limit J ‐spaces corresponding to the general real method. These interpolation spaces are defined by Banach sequence lattices and include those spaces that arise by the choice θ = 0 in the definition of the real method. We pay especial attention to spaces generated by rearrangement‐invariant sequence spaces. We establish necessary and sufficient conditions for compactness of interpolated operators between limit J ‐spaces. We also study the relationships between J ‐ and K ‐spaces and we derive some interpolation formulae for notable couples of function spaces, couples of spaces of operators and also couples of sequence spaces.