Noninvertibility preservers on Banach algebras
It is proved that a linear surjection , which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.
Preserving zeros of Lie product on alternate matrices
We study continuous maps on alternate matrices over complex field which preserve zeros of Lie product.
Maximal abelian subalgebras of
Let be an infinite dimensional complex Banach space and be the Banach algebra of all bounded linear operators on . Żelazko [1] posed the following question: Is it possible that some maximal abelian subalgebra of is finite dimensional? Interestingly, he was able to show that there does exist an infinite dimensional closed subalgebra of 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...
Additive rank-one nonincreasing maps on Hermitian matrices over the field .
General preservers of quasi-commutativity on Hermitian matrices.
Tracial numerical ranges and linear dependence of operators.
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