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An infinite dimensional Banach algebra with all but one maximal abelian subalgebras of dimension two. (English) Zbl 1190.46038

It is known that if all maximal abelian subalgebras of an algebra are finite-dimensional, then the algebra itself is of finite dimension; cf.W.Żelazko [PLISKA, Stud.Math.Bulg.11, 113–116 (1991; Zbl 0773.46024)]. In the paper under review, the author constructs an infinite-dimensional Banach algebra whose all but one maximal abelian subalgebras are of finite dimension two.

MSC:

46H10 Ideals and subalgebras

Citations:

Zbl 0773.46024
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