The Triangle of Operators, Topologies, Bornologies
نویسنده
چکیده
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.
منابع مشابه
ar X iv : m at h / 05 06 18 3 v 1 [ m at h . FA ] 1 0 Ju n 20 05 THE TRIANGLE OF OPERATORS , TOPOLOGIES , BORNOLOGIES
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 (vi...
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