Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Varieties of linear topological spaces

Authors: J. Diestel, Sidney A. Morris and Stephen A. Saxon
Journal: Trans. Amer. Math. Soc. 172 (1972), 207-230
MSC: Primary 46A05; Secondary 46B99, 46M15
MathSciNet review: 0316992
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Abstract: This paper initiates the formal study of those classes of locally convex spaces which are closed under the taking of arbitrary subspaces, separated quotients, cartesian products and isomorphic images. Well-known examples include the class of all nuclear spaces and the class of all Schwartz spaces.

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Keywords: Products, subspaces of locally convex spaces, quotients of locally convex spaces, Banach spaces, Fréchet spaces, nuclear spaces, Schwartz spaces, reflexivity, separability, weak topology, strongest locally convex topology, $ {l_1}(\Gamma ),{l_p},{L_p},{c_0}$ spaces of continuous functions, singly generated variety, universal generator
Article copyright: © Copyright 1972 American Mathematical Society