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Some generalizations of Kadison's theorem: a survey.

T. S. S. R. K. Rao (2004)

Extracta Mathematicae

Motivated by a well-known result of Kadison that describes surjective isometries of the space of compact and the space of bounded operators on a Hilbert space, in this paper we investigate the structure of surjective isometries on the space of compact and on the space of bounded operators between Banach spaces. We give an example to show that isometries in general need not be of the canonical form. As an application of our study of the group of isometries, we consider the algebraic reflexivity of...

Some results about absolute summability of operators in Banach spaces.

Luis López Corral (1986)

Stochastica

In order to study the absolute summability of an operator T we consider the set ST = {{xn} | ∑||Txn|| < ∞}. It is well known that an operator T in a Hilbert space is nuclear if and only if ST contains an orthonormal basis and it is natural to ask under which conditions two orthonormal basis define the same left ideal of nuclear operators. Using results about ST we solve this problem in the more general context of Banach spaces.

Some results on (strong) asymptotic Toeplitzness and Hankelness

Mehdi Nikpour (2019)

Czechoslovak Mathematical Journal

Based on the results in A. Feintuch (1989), this work sheds light upon some interesting properties of strongly asymptotically Toeplitz and Hankel operators, and relations between these two classes of operators. Indeed, among other things, two main results here are (a) vanishing Toeplitz and Hankel operators forms an ideal, and (b) finding the distance of a strongly asymptotically Toeplitz operator from the set of vanishing Toeplitz operators.

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