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Linear mappings between topological vector spaces

Published online by Cambridge University Press:  09 April 2009

B. D. Craven
B. D. Craven
Affiliation:
Department of Mathematics, Melbourne UniversityVictoria, 3052, Australia
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If A and B are locally convex topological vector spaces, and B has certain additional structure, then the space L(A, B) of all continuous linear mappings of A into B is characterized, within isomorphism, as the inductive limit of a family of spaces, whose elements are functions, or measures. The isomorphism is topological if L(A, B) is given a particular topology, defined in terms of the seminorms which define the topologies of A and B. The additional structure on B enables L(A, B) to be constructed, using the duals of the normed spaces obtained by giving A the topology of each of its seminorms separately.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 105 - 118
Copyright
Copyright © Australian Mathematical Society 1972

References

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