The triangle of operators, topologies, bornologies

Details The triangle of operators, topologies, bornologies The triangle of operators, topologies, bornologies

2005-06-10

arxiv.org/abs/math/0506183v1

Mathematics

Functional Analysis

33 pages

Scientific paper

This paper discusses two common techniques in functional analysis: the topological method and the bornological method. In terms of Pietsch's operator ideals, we establish the equivalence of the notions of operators, topologies and bornologies. The approaches in the study of locally convex spaces of Grothendieck (via Banach space operators), Randtke (via continuous seminorms) and Hogbe-Nlend (via convex bounded sets) are compared.

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