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Preserving zeros of Lie product on alternate matrices

100%

Fošner A., Kuzma B.

Special Matrices

2016

tom 4

nr 1

80-100

We study continuous maps on alternate matrices over complex field which preserve zeros of Lie product.

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Maximal abelian subalgebras of \(B(\mathcal{X})\)

100%

Bračič J., Kuzma B.

Commentationes Mathematicae

2008

tom 48

nr 1

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 \(\text{dim} X = \infty\).

Ograniczanie wyników

1 Commentationes Mathematicae

1 Special Matrices

2 Kuzma B.

1 Bračič J.

1 Fošner A.

1 2016

1 2008

Wyniki wyszukiwania

Preserving zeros of Lie product on alternate matrices

Maximal abelian subalgebras of \(B(\mathcal{X})\)