Maximal abelian subalgebras of B(X)

• Autorzy: Bračič J. , Kuzma B.
• Języki publikacji: EN

Abstrakty

EN

Let X be an infinite dimensional complex Banach space and B(X) be the Banach algebra of all bounded linear operators on X. Zelazko [1] posed the following question: Is it possible that some maximal abelian subalgebra of B(X) is finite dimensional? Interestingly, he was able to show that there does exist an infinite dimensional closed subalgebra of B(X) with all but one maximal abelian subalgebras of dimension two. The aim of this note is to give a negative answer to the original question and prove that there does not exist a finite dimensional maximal commutative subalgebra of B(X) if dimX = ∞.

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: 95--98
• Opis fizyczny: bibliogr. 1 poz.

Twórcy

autor

Bračič J.

autor

Kuzma B.

• University of Ljubljana, IMFM Jadranska ul. 19, SI-1000 Ljubljana, Slovenia,

Bibliografia

• [1] W. Żelazko: Private communication.