Żelazko, Wiesław An infinite dimensional Banach algebra with all but one maximal abelian subalgebras of dimension two. (English) Zbl 1190.46038 Commentat. Math. 48, No. 1, 99-101 (2008). 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. Reviewer: Mohammad Sal Moslehian (Mashhad) Cited in 2 Documents MSC: 46H10 Ideals and subalgebras Keywords:abelian algebra; bounded operators; complex Banach space Citations:Zbl 0773.46024 PDFBibTeX XMLCite \textit{W. Żelazko}, Commentat. Math. 48, No. 1, 99--101 (2008; Zbl 1190.46038)