On vector spaces and algebras with maximal locally pseudoconvex topologies
Studia Mathematica, Tome 112 (1994) no. 2, pp. 195-201
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Let X be a real or complex vector space. We show that the maximal p-convex topology makes X a complete Hausdorff topological vector space. If X has an uncountable dimension, then different p give different topologies. However, if the dimension of X is at most countable, then all these topologies coincide. This leads to an example of a complete locally pseudoconvex space X that is not locally convex, but all of whose separable subspaces are locally convex. We apply these results to topological algebras, considering the problem of uniqueness of a complete topology for semitopological algebras and giving an example of a complete locally convex commutative semitopological algebra without multiplicative linear functionals, but with every separable subalgebra having a total family of such functionals.
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author = {A. Kokk and W. \.Zelazko},
title = {On vector spaces and algebras with maximal locally pseudoconvex topologies},
journal = {Studia Mathematica},
pages = {195--201},
publisher = {mathdoc},
volume = {112},
number = {2},
year = {1994},
doi = {10.4064/sm-112-2-195-201},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-112-2-195-201/}
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A. Kokk; W. Żelazko. On vector spaces and algebras with maximal locally pseudoconvex topologies. Studia Mathematica, Tome 112 (1994) no. 2, pp. 195-201. doi: 10.4064/sm-112-2-195-201
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