Local Spectrum, Local Spectral radius,and Growth Conditions
In this paper we present complete description of the elements of Banach space with one-point spectrum. Some applications of these results are also given.
math.FA↗
arXiv subjects
Heybetkulu Mustafayev
Publications and source records attributed to Heybetkulu Mustafayev.
Some Convergence Theorems for Operator Sequences
Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and $\left\{ \frac{1}{n}\sum_{i=0}^{n-1}A^{i}TB^{i}% \right\} $. These results are applied to the Toeplitz, composition and model operators. Some related problems are also discussed.
math.FA↗
Operators Whose Conjugation Orbits Satisfy Polynomial Growth Conditions
Let $A$ be a bounded linear operator on a complex Banach space $X.$ For a given $α\geq 0,$ we consider the class $\mathcal{D}_{A}^{α}\left( \mathbb{R} \right) $ of all bounded linear operators $T$ on $X$ for which there exists a constant $C_{T}>0$, such that \begin{equation*} \left\Vert e^{tA}Te^{-tA}\right\Vert \leq C_{T}\left( 1+\left\vert t\right\vert \right) ^{α}, \text {} \forall t\in \mathbb{R} \end{equation*} We present complete description of the class $\mathcal{D}_{A}^{α}\left( \mathbb{R} \right) $ in the case when the spectrum of $A$ consists of one point. These results are linked to the decomposability of $A.$ Some estimates for the norm of the commutator $AT-TA$ are obtained in the case $0\leq α<1.$
math.FA↗