arXiv subjects

Ivan S. Feshchenko

Publications and source records attributed to Ivan S. Feshchenko.

3 recordsLinked to original sources

arXiv2013

On the closedness of the sum of ranges of operators $A_k$ with almost compact products $A_i^* A_j$

Let $\mathcal{H}_1,\ldots,\mathcal{H}_n,\mathcal{H}$ be complex Hilbert spaces and $A_k:\mathcal{H}_k\to\mathcal{H}$ be a bounded linear operator with the closed range $Ran(A_k)$, $k=1,\ldots,n$. It is known that if $A_i^*A_j$ is compact for any $i\neq j$, then $\sum_{k=1}^n Ran(A_k)$ is closed. We show that if all products $A_i^*A_j$, $i\neq j$ are "almost" compact, then the subspaces $Ran(A_1),\ldots,Ran(A_n)$ are essentially linearly independent and their sum is closed.

math.FA↗

arXiv2013

On the essential spectrum of the sum of self-adjoint operators and the closedness of the sum of operator ranges

We get a criterion for 0 to be in the essential spectrum of a sum of self-adjoint operators whose pairwise products are compact. Using this result, we obtain necessary and sufficient conditions for the sum of ranges of such operators to be closed.

math.FA↗

arXiv2012

On absolutely representing families of subspaces in Banach spaces

An absolutely representing family of subspaces is a natural generalization of an absolutely representing system of subspaces and absolutely representing system (of elements). We obtain necessary an (or) sufficient conditions for a family of subspaces to be an absolutely representing family of subspaces and study properties of absolutely representing families of subspaces in Banach spaces. As an example, we study families of subspaces spanned by exponents.

math.FA↗