A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.

W. Żelazko

Studia Mathematica (1996)

  • Volume: 119, Issue: 2, page 195-198
  • ISSN: 0039-3223

Abstract

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We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].

How to cite

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Żelazko, W.. "A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.." Studia Mathematica 119.2 (1996): 195-198. <http://eudml.org/doc/216294>.

@article{Żelazko1996,
abstract = {We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].},
author = {Żelazko, W.},
journal = {Studia Mathematica},
keywords = {topological algebra; -convex; complete multiplicatively convex algebras; maximal commutative subalgebras; non-metrizable; non-Banach},
language = {eng},
number = {2},
pages = {195-198},
title = {A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.},
url = {http://eudml.org/doc/216294},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Żelazko, W.
TI - A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 2
SP - 195
EP - 198
AB - We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].
LA - eng
KW - topological algebra; -convex; complete multiplicatively convex algebras; maximal commutative subalgebras; non-metrizable; non-Banach
UR - http://eudml.org/doc/216294
ER -

References

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  1. [1] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981. Zbl0466.46001
  2. [2] A. Kokk and W. Żelazko, On vector spaces and algebras with maximal locally pseudoconvex topologies, Studia Math. 112 (1995), 195-201. Zbl0837.46037
  3. [3] E. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952). Zbl0047.35502
  4. [4] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1971. 
  5. [5] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, New York, 1978. Zbl0395.46001
  6. [6] W. Żelazko, Selected Topics in Topological Algebras, Aarhus Univ. Lecture Notes No 31 (1971). Zbl0221.46041
  7. [7] W. Żelazko, On certain open problems in topological algebras, Rend. Sem. Mat. Fis. Milano 59 (1989), 1992, 49-58. Zbl0755.46019
  8. [8] W. Żelazko, Concerning entire functions in B 0 -algebras, Studia Math. 110 (1994), 283-290. Zbl0803.46051

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