Topological amenability and Köthe co-echelon algebras

DOI10.1007/s43037-021-00163-5zbMath1494.46044arXiv2012.08956OpenAlexW4205217837MaRDI QIDQ2073153

Krzysztof Piszczek, A. Yu. Pirkovskii

Publication date: 27 January 2022

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.08956

zbMATH Keywords

projective moduleamenable algebraflat moduleDF-spaceDF-algebraKöthe co-echelon algebraKöthe co-echelon space

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) General theory of topological algebras (46H05) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Locally convex Fréchet spaces and (DF)-spaces (46A04) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) Tensor products in functional analysis (46M05)

Cites Work

• Homology and cohomology for topological algebras
• A general framwork for a multi-operator functional calculus
• Cyclic cohomology of certain nuclear Fréchet algebras and \(DF\) algebras
• Flat cyclic Fréchet modules, amenable Fréchet algebras, and approximate identities
• Complete projective tensor product of (LB)-spaces
• Derived categories for functional analysis
• Derived functors in functional analysis
• Ein einfacher Beweis des Kohärenzsatzes von Grauert. (A simple proof of Grauert's coherence theorem)
• Köthe coechelon spaces as locally convex algebras
• Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras
• Weak homological dimensions and biflat Köthe algebras
• Higher algebraic K-theory: I
• Algebras of holomorphic functions with Hadamard multiplication
• Contractible Köthe co-echelon algebras
• Amenable Köthe co‐echelon algebras
• Amenable Banach Algebras
• Homological methods in the theory of locally convex spaces
• Cohomology in Banach algebras
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