An infinite dimensional Banach algebra with all but one maximal abelian subalgebras of dimension two

• Autorzy: Żelazko W.
• Języki publikacji: EN

Abstrakty

EN

I construct a unital closed subalgebra of L(H) with the property announced in the title. Moreover, for any two maxiamal abelian subalgebras of the algebra in question, their intersection consists only of scalar multiples of the unity.

Słowa kluczowe

EN

Abelian algebra; bounded operators; complex Banach space

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2008
• Tom: Vol. 48, [Z] 1
• Strony: 99--101
• Opis fizyczny: bibliogr. 3 poz.

Twórcy

autor

Żelazko W.

• Mathematical Institute, Polish Academy of Sciences Śniadeckich 8, P.O. Box 21, 00-956 Warsaw, Poland,

Bibliografia

• [1] J. Bračič and B. Kuzma, Maximal abelian subalgebras of B(X), Commentationes Mathematicae 48.1 (2008), 95-98.
• [2] T. J. Laffey, Commutative subalgebras of infinite dimensional algebras, Bull. London. Math. Soc. 5 (1973), 312-314.
• [3] W. Żelazko,Concerning trivial maximal abelian subalgebras of B(X), Pliska Studia Math. Bulg. 11 (1991), 113-116.