Related papers: Characteristic function of a power partial isometr…
A particular case of results from [K2] is as follows. Let the unitary asymptote of a contraction $T$ contain the bilateral shift (of finite or infinite multiplicity). Then there exists an invariant subspace $\mathcal M$ of $T$ such that…
The purpose of this paper is two-fold: firstly, we give a characterization on the level of non-unital operator systems for when the zero map is a boundary representation. As a consequence, we show that a non-unital operator system arising…
A contractive $n$-tuple $A=(A_1,...,A_n)$ has a minimal joint isometric dilation $S=(S_1,...,S_n)$ where the $S_i$'s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When $A$…
In this paper, we characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on weighted Fock-Sobolev spaces of fractional order.
We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…
For $-1\le B<A\le 1$, let $\mathcal{S}^*(A,B)$ denote the class of normalized analytic functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in $|z|<1$ which satisfy the subordination relation $zf'(z)/f(z)\prec (1+Az)/(1+Bz)$ and $\Sigma^*(A,B)$…
We introduce a new class of conjugations and characterize complex symmetric Toeplitz operators on the Hardy space with respect to those conjugations. Also, we prove that complex symmetricity and \uet~ property are the same for a certain…
A generalization of Powers-St$\o$rmer's inequality for operator monotone functions on $[0, +\infty)$ and for positive linear functional on general $C^*$-algebras will be proved. It also will be shown that the generalized Powers-St$\o$rmer…
We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $\psi(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent…
This article investigates $k$-regular factorizations of characteristic functions associated with completely non-coisometric row contractions. In this setting, a one-to-one correspondence is established between chains of joint invariant…
This paper discusses the properties of a modified version of the Stancu variant Sz\'asz-Mirakjan Kantorovich type operators. We determine the order of approximation in terms of the modulus of continuity and second-order of smoothness, and…
In this paper, we study subclass of analytic function with negative coefficient defined by integral operator in the unit disc $U = \left\{ {z \in C:\left| z \right| < 1} \right\}$. The results are included coefficient estimates, closure…
We investigate the commutativity and semi-commutativity of generalized singular integral operators of the form $P_{+} f P_{+} + P_{-} g P_{+} + P_{+} u P_{-} + P_{-} v P_{-}$ on $L^{2}$, where $P_{+}$ denotes the Riesz projection and…
Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs…
In this paper we study canonical models for representations of the Hardy algebras that generalize the model theory of Sz.-Nagy and Foias for contraction operators. The Hardy algebras are non selfadjoint operator algebras associated with…
We introduce and study a scale of operator classes on the annulus that is motivated by the $\mathcal{C}_{\rho}$ classes of $\rho$-contractions of Nagy and Foia\c{s}. In particular, our classes are defined in terms of the contractivity of…
For any bounded domain $\Omega$ in $\mathbb C^m,$ let ${\mathrm B}_1(\Omega)$ denote the Cowen-Douglas class of commuting $m$-tuples of bounded linear operators. For an $m$-tuple $\boldsymbol T$ in the Cowen-Douglas class ${\mathrm…
Truncated Toeplitz operators are C--symmetric with respect to the canonical conjugation given on an appropriate model space. However, by considering only one conjugation one cannot characterize truncated Toeplitz operators. It will be…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a…