Banach space techniques underpinning a theory for nearly additive mappings
Copyright policy )Banach space techniques underpinning a theory for nearly additive mappings
In this very interesting paper the authors make a first attempt towards an understanding of the connections between Ulam's stability problem for additive maps and the theory of extension of Banach spaces. The content of the paper is indicated by the titles of chapters: -- Ulam's stability problem and twisted sums: two faces of a coin; -- Nearly additive mappings on controlled groups; -- Uniform boundedness principles; -- Asymptotically additive maps; -- Nearly additive mappings and exact sequences; -- Duality theory and localization techniques; -- Homology sequences and applications.
Projective and injective objects in functional analysis, Stability, separation, extension, and related topics for functional equations, duality theory, nearly additive mappings, controlled groups, Categories, functors in functional analysis, uniform boundedness principles, extension of Banach spaces, twisted sums, Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.), Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), exact sequences, Functional inequalities, including subadditivity, convexity, etc., Ultraproducts in functional analysis, Ulam's stability, homology sequences, asymptotically additive mappings
Projective and injective objects in functional analysis, Stability, separation, extension, and related topics for functional equations, duality theory, nearly additive mappings, controlled groups, Categories, functors in functional analysis, uniform boundedness principles, extension of Banach spaces, twisted sums, Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.), Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), exact sequences, Functional inequalities, including subadditivity, convexity, etc., Ultraproducts in functional analysis, Ulam's stability, homology sequences, asymptotically additive mappings
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