Banach space techniques underpinning a theory for nearly additive mappings

DOI10.4064/dm404-0-1zbMath1035.39018OpenAlexW1965356920MaRDI QIDQ4791462

Félix Cabello Sánchez, Jesús M. Fernandez Castillo

Publication date: 28 January 2003

Published in: Dissertationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/dm404-0-1

zbMATH Keywords

exact sequencesduality theorytwisted sumsuniform boundedness principlesUlam's stabilityhomology sequencesnearly additive mappingsasymptotically additive mappingscontrolled groupsextension of Banach spaces

Mathematics Subject Classification ID

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Stability, separation, extension, and related topics for functional equations (39B82) Ultraproducts in functional analysis (46M07) Projective and injective objects in functional analysis (46M10) Functional inequalities, including subadditivity, convexity, etc. (39B62) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) Categories, functors in functional analysis (46M15)

Related Items (9)

Lipschitz structure of quasi-Banach spaces ⋮ On sandwich theorem for delta-subadditive and delta-superadditive mappings ⋮ Stability of vector measures and twisted sums of Banach spaces ⋮ The Khinchin-Kahane and Lévy inequalities for abelian metric groups, and transfer from normed (abelian semi)groups to Banach spaces ⋮ Functional Equations and Stability Problems on Hypergroups ⋮ Variants on the Berz sublinearity theorem ⋮ Linear mappings approximately preserving orthogonality ⋮ Strictly singular quasi-linear maps ⋮ The singular case in the stability of additive functions

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