This is an announcement for the paper "The triangle of operators, topologies, bornologies" by Ngai-Ching Wong.

Abstract: 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.

Archive classification: Functional Analysis; Operator Algebras

Mathematics Subject Classification: 47L20, 46A03, 46A11, 46A17

Remarks: 33 pages

The source file(s), triangle05_ArXiV.tex: 98877 bytes, is(are) stored in gzipped form as 0506183.gz with size 27kb. The corresponding postcript file has gzipped size 124kb.

Submitted from: wong@math.nsysu.edu.tw

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