Exact subcategories of the category of locally convex spaces

DOI10.1002/mana.201100325zbMath1276.18011OpenAlexW2060773647MaRDI QIDQ4902783

Dennis Sieg, Bernhard Dierolf

Publication date: 17 January 2013

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201100325

zbMATH Keywords

locally convex spacesexact structuretopologically exact sequencesthree-space-property

Mathematics Subject Classification ID

Nonabelian homological algebra (category-theoretic aspects) (18G50) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) Abelian categories, Grothendieck categories (18E10)

Related Items

The heart of the Banach spaces ⋮ The left heart and exact hull of an additive regular category ⋮ Local, colocal, and antilocal properties of modules and complexes over commutative rings ⋮ A homological approach to the splitting theory of \(\mathrm{PLS}_{\mathrm{w}}\) spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the three-space-problem for topological vector spaces
• On the three-space-problem and the lifting of bounded sets
• Derived functors in functional analysis
• The mathematical work of Susanne Dierolf
• The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations
• Projective and injective limits of weakly compact sequences of locally convex spaces
• Exact categories
• On the "Three space problem".
• Examples for the Nonlocally Convex Three Space Problem
• Stefan Heinrich's Density Condition for Fréchet Spaces and the Characterization of the Distinguished Köthe Echelon Spaces
• A splitting theory for the space of distributions
• A counterexample to Raikov's conjecture
• Homological methods in the theory of locally convex spaces