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Topologies and bornologies determined by operator ideals, II

Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43669

Studia Math, 111, (2), 153-162, 1994
Let A be an operator ideal on LCSs. A continuous seminorm p of a LCS X is said to be Acontinuous if Qp Ainj (X, Xp), where Xp is the completion of the normed space Xp= X/p 1 (0) and Qp is the canonical map. p is said to be a Groth (A)seminorm if there is a continuous seminorm q of X such that p q and the canonical map Qpq: Xq Xp belongs to A (Xq, Xp). It is well-known that when A is the ideal of absolutely summing (resp. precompact, weakly compact) operators, a LCS X is a nuclear (resp. Schwartz, infraSchwartz) space if and only if every continuous seminorm p of X is Acontinuous if and only if every continuous seminorm p of X is a Groth (A)seminorm. In this paper, we extend this equivalence to arbitrary operator ideals A and discuss several aspects of these constructions which are initiated by A. Grothendieck and D. Randkte, respectively. A bornological version of the theory is obtained, too.
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@inproceedings{ngai-ching1994topologies,
  title={Topologies and bornologies determined by operator ideals, II},
  author={Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210124052876198},
  booktitle={Studia Math},
  volume={111},
  number={2},
  pages={153-162},
  year={1994},
}
Ngai-Ching Wong. Topologies and bornologies determined by operator ideals, II. 1994. Vol. 111. In Studia Math. pp.153-162. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210124052876198.
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