The triangle of operators, topologies, bornologies

Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43689

arXiv preprint math/0506183, 2005.6
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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  title={The triangle of operators, topologies, bornologies},
  author={Ngai-Ching Wong},
  booktitle={arXiv preprint math/0506183},
Ngai-Ching Wong. The triangle of operators, topologies, bornologies. 2005. In arXiv preprint math/0506183.
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