Browsing by Subject "compact operators"

Now showing 1 - 5 of 5

Access status: Open Access ,
Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces
(Wydawnictwa AGH, 2020) Lo, Ching-on; Loh, Anthony Wai-keung
Let $u$ and $\varphi$ be two analytic functions on the unit disk $\mathbb{D}$ such that $\varphi\mathbb{D} \subset \mathbb{D}$. A weighted composition operator $uC_{\varphi}$ induced by $u$ and $\varphi$ is defined on $H^2$, the Hardy space of $\mathbb{D}$, by $uC_{\varphi}f := u \cdot f \circ \varphi$ for every $f$ in $H^2$. We obtain sufficient conditions for Hilbert-Schmidtness of $uC_{\varphi}$ on $H^2$ in terms of function-theoretic properties of $u$ and $\varphi$. Moreover, we characterize Hilbert-Schmidt difference of two weighted composition operators on $H^2$.
Access status: Open Access ,
Hyponormal differential operators with discrete spectrum
(2010) Ismailov, Zameddin I.; Unluyol, Erdal
In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
Access status: Open Access ,
Inequalities for regularized determinants of operators with the Nakano type modulars
(2013) Gil', Mihail Iosifovič
Let $\{p_k\}$ be a nondecreasing sequence of integers, and $A$ be a compact operator in a Hilbert space whose eigenvalues and singular values are $\lambda_k(A)$ and $s_k(A)$ $(k=1, 2, .... )$, respectively. We establish upper and lower bounds for the regularized determinant $\prod_{k=1}^\infty (1-\lambda_k(A)){\rm exp}\;[\sum_{m=1}^{p_k-1} \frac{\lambda_k^m(A)}{m}],\mbox{ assuming that } \sum_{j=1}^{\infty} \frac{s_j^{p_j}(A/c)}{p_j}\lt \infty$ for a constant $c\in (0,1)$.
Access status: Restricted ,
Nierówności wyrocznie dla problemów odwrotnych
(Data obrony: 2018-09-05) Mika, Grzegorz
Wydział Matematyki Stosowanej
Access status: Restricted ,
Wybrane własności operatorów Hilberta-Schmidta
(Data obrony: 2017-07-12) Różycki, Radosław
Wydział Matematyki Stosowanej