Journals / Turkish Journal of Mathematics / 2007 / Cilt: 31 - Sayı: 1
Traces of Maximal Ideals of Topological Algebras in Their Subalgebras
- Pages
- 79–88
- DOI
- —
Abstract
Let K be one of the fields R or C, A a topological associative algebra over K with separately continuous multiplication, B a subalgebra of A and M a closed maximal regular left (right or two-sided) ideal of A such that the trace M \cap B of M is a proper subset of B. In cases, when B is a Gelfand-Mazur subalgebra of A or a subalgebra of the centre Z(A) of A, such classes of topological algebras in which M \cap B (in the subset topology) is a closed maximal regular left (respectively, right or two-sided) ideal of B, are described.
Özet
Let K be one of the fields R or C, A a topological associative algebra over K with separately continuous multiplication, B a subalgebra of A and M a closed maximal regular left (right or two-sided) ideal of A such that the trace M \cap B of M is a proper subset of B. In cases, when B is a Gelfand-Mazur subalgebra of A or a subalgebra of the centre Z(A) of A, such classes of topological algebras in which M \cap B (in the subset topology) is a closed maximal regular left (respectively, right or two-sided) ideal of B, are described.