Inductive limits and ε-tensor products.

DOI10.1515/crll.1980.319.38zbMath0426.46053OpenAlexW4246992203MaRDI QIDQ3861969

Ralf Hollstein

Publication date: 1980

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002197693

zbMATH Keywords

weighted spaceshereditary propertiesnuclear spaceinductive limitsepsilon-tensor productsDF-spaceepsilon-spacecountable locally convex direct sumsNachbin family of continuous functionsscript L infinity spaceweighted spaces of continuous functions with values in an inductive limit

Mathematics Subject Classification ID

Topological linear spaces of continuous, differentiable or analytic functions (46E10) Locally convex Fréchet spaces and (DF)-spaces (46A04) Inductive and projective limits in functional analysis (46M40) Tensor products in functional analysis (46M05)

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Tensor products and spaces of vector-valued continuous functions ⋮ Bornological and ultrabornological spaces of typ \(C(X,F)\) and \(E \in F\) ⋮ Permanence properties of C(X,E) ⋮ Barrelledness and bornological conditions on spaces of vector-valued \(\mu\)-simple functions ⋮ On the injective tensorproduct of (DF)-spaces ⋮ Weighted PLB-spaces of continuous functions arising as tensor products of a Fréchet and a DF-space ⋮ A Projective Description of Weighted Inductive Limits ⋮ Characterization of the maximal ideal of operators associated to the tensor norm defined by an Orlicz function ⋮ A Hahn-Banach theorem for holomorphic mappings on localy convex spaces ⋮ The countable neighbourhood property and tensor products ⋮ On weighted inductive limits of spaces of continuous functions ⋮ Tensor sequences and inductive limits with local partition of unity ⋮ The Hilbert tensor product and inductive limits ⋮ An extension and lifting theorem for bounded linear mappings in locally convex spaces and some applications

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