Temat: Banach algebra - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: An infinite dimensional Banach algebra with all but one maximal abelian subalgebras of dimension two
Autorzy:: Żelazko, Wiesław
Powiązania:: https://bibliotekanauki.pl/articles/960131.pdf
Data publikacji:: 2008
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Abelian algebra
Bounded operators
Complex Banach space
Opis:: 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.
Źródło:: Commentationes Mathematicae; 2008, 48, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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

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