Related papers: Centered weighted composition operators on $L^2$-s…
In this paper, we prove that the null space of a weighted composition operator on $\ell_p~ (1 \leq p < \infty)$ is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on $\ell_p$…
A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
In a paper from 2012 Jab{\l}o\'nski, Jung and Stochel introduced the weighted shifts on directed trees, a generalisation of well known weighted shift operators on $\ell^2$. In the last decade this class has proven itself handy for finding…
In this paper we define $\lambda$-hyponormal operators on an infinite dimensional Hilbert space $\mathcal{H}$ and find a class of $\lambda$-hyponormal operators that can not be hypercyclic. Also, we study closedness of range and…
In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.
The weighted shifts are long known and important class of operators. One of known generalisation of this class are weighted shifts on directed trees, where we replace the linear order of coordinates in $\ell^2$ with a possibly more…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…
In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson…
This dissertation summarizes my investigations in operator theory during my PhD studies. The first chapter is an introduction to that field of operator theory which was developed by B. Sz.-Nagy and C. Foias, the theory of power-bounded…
Let $\mathscr T$ be a rooted directed tree with finite branching index $k_{\mathscr T}$ and let $S_{\lambda} \in B(l^2(V))$ be a left-invertible weighted shift on ${\mathscr T}$. We show that $S_{\lambda}$ can be modelled as a…
In this paper, some characterizations for the compact difference of composition operators on Bergman spaces $A^p_\omega$ with doubling weight are given, which extend Moorhouse's characterization for the difference of composition operators…
We provide complete characterisations of nuclear weighted composition operators between two distinct $L^p(\mu)$-spaces, where $1\leq p<\infty$. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted…
We characterize the spectra of composition operators on the Hardy space $H^2(B_N)$, when the symbols are elliptic or hyperbolic linear fractional self-maps of $B_N$. Therefore, combining with the result obtained by Bayart \cite{B10}, the…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal…
Let $\omega$ be an unbounded radial weight on $\mathbb{C}^d$, $d\ge 1$. Using results related to approximation of $\omega$ by entire maps, we investigate Volterra type and weighted composition operators defined on the growth space…
We investigate the bounded composition operators induced by linear fractional self-maps of the right half-plane $\mathbb{C}_+$ on the Hardy space $H^2(\mathbb{C}_+).$ We completely characterize which of these operators are cohyponormal and…