2019
Том 71
№ 9

All Issues

Rashid M. H. M.

Articles: 3
Article (English)

Stability of versions of the Weyl-type theorems under tensor product

Prasad T., Rashid M. H. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 542-550

We study the transformation versions of the Weyl-type theorems from operators $T$ and $S$ for their tensor product $T \otimes S$ in the infinite-dimensional space setting.

Brief Communications (English)

Generalized Weyl's theorem and tensor product

Rashid M. H. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 9. - pp. 1289-1296

We give necessary and/or sufficient conditions ensuring the passage of generalized a-Weyl theorem and property $(gw)$ from $A$ and $B$ to $A \otimes B$.

Article (English)

Weyl's theorem for algebrascally $wF(p, r, q)$ operators with $p, q > 0$ and $q \geq 1$

Rashid M. H. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1092-1102

If $T$ or $T*$ is an algebraically $wF(p, r, q)$ operator with $p, r > 0$ and $q ≥ 1$ acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for $f(T)$, for every $f \in \text{Hol}(\sigma(T))$, where $ \text{Hol}(\sigma(T))$ denotes the set of all analytic functions in an open neighborhood of $\sigma(T)$. Moreover, if $T^*$ is a $wF(p, r, q)$ operator with $p, r > 0$ and $q ≥ 1$, then the $a$-Weyl theorem holds for $f(T)$. Also, if $T$ or $T^*$ is an algebraically $wF(p, r, q)$ operators with $p, r > 0$ and $q ≥ 1$, then we establish spectral mapping theorems for the Weyl spectrum and essential approximate point spectrum of T for every $f \in \text{Hol}(\sigma(T))$, respectively. Finally, we examine the stability of the Weyl theorem and $a$-Weyl theorem under commutative perturbation by finite-rank operators.