- Tytuł:
- Maximal abelian subalgebras of \(B(\mathcal{X})\)
- Autorzy:
-
Bračič, Janko
Kuzma, Bojan - Powiązania:
- https://bibliotekanauki.pl/articles/746718.pdf
- Data publikacji:
- 2008
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Abelian algebra
Bounded operators
Complex Banach space - Opis:
- Let \(\mathcal{X}\) be an infinite dimensional complex Banach space and \(B(\mathcal{X})\) be the Banach algebra of all bounded linear operators on \(\mathcal{X}\). Żelazko [1] posed the following question: Is it possible that some maximal abelian subalgebra of \(B(\mathcal{X})\) is finite dimensional? Interestingly, he was able to show that there does exist an infinite dimensional closed subalgebra of \(B(\mathcal{X})\) 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 \(B(\mathcal{X})\) if \(\text{dim} X = \infty\).
- Źródło:
-
Commentationes Mathematicae; 2008, 48, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł