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

• Autorzy: W. Żelazko
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 46H10: Ideals and subalgebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 119
• Numer: 2
• Strony: 195-198

Daty

wydano

1996

otrzymano

1996-03-29

poprawiono

1996-04-09

Twórcy

autor

W. Żelazko

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137 00-950 Warszawa, Poland

Bibliografia

• [1] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981.
• [2] A. Kokk and W. Żelazko, On vector spaces and algebras with maximal locally pseudoconvex topologies, Studia Math. 112 (1995), 195-201.
• [3] E. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952).
• [4] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1971.
• [5] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, New York, 1978.
• [6] W. Żelazko, Selected Topics in Topological Algebras, Aarhus Univ. Lecture Notes No 31 (1971).
• [7] W. Żelazko, On certain open problems in topological algebras, Rend. Sem. Mat. Fis. Milano 59 (1989), 1992, 49-58.
• [8] W. Żelazko, Concerning entire functions in $B_0$-algebras, Studia Math. 110 (1994), 283-290.