Related papers: Bishop-like theorems for non-subnormal operators

This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…

The 6d $\mathcal{N}=(2,0)$ theory has natural surface operator observables, which are akin in many ways to Wilson loops in gauge theories. We propose a definition of a "locally BPS" surface operator and study its conformal anomalies, the…

A commuting triple of Hilbert space operators $(A,S,P)$ is said to be a \textit{$\mathbb{P}$-contraction} if the closed pentablock $\overline{\mathbb P}$ is a spectral set for $(A,S,P)$, where \[ \mathbb{P}:=\left\{(a_{21}, \mbox{tr}(A_0),…

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2…

The unitary equivalence of $2$-isometric operators satisfying the so-called kernel condition is characterized. It relies on a model for such operators built on operator valued unilateral weighted shifts and on a characterization of the…

To each graph on $n$ vertices there is an associated subspace of the $n \times n$ matrices called the operator system of the graph. We prove that two graphs are isomorphic if and only if their corresponding operator systems are unitally…

Let $X,Y$ be normal bounded operators on a Hilbert space such that $e^X=e^Y$. If the spectra of $X$ and $Y$ are contained in the strip $\s$ of the complex plane defined by $|\Im(z)|\leq \pi$, we show that $|X|=|Y|$. If $Y$ is only assumed…

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $\phi$ and $\psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such…

This paper addresses the isomorphism problem for the universal (nonself-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if…

There are considered isometries on a Hilbert space. By the Wold theorem any isometry can be decomposed into a unitary operator and a unilateral shift. For a pair of isometries, even commuting, a maximal subspace reducing one isometry to a…

An operator T on Hilbert space is a 3-isometry if there exists operators B and D such that (T*)^n T^n = I+nB +n^2 D. An operator J is a Jordan operator if it the sum of a unitary U and nilpotent N of order two which commute. If T is a…

In the present paper, we generalized some notions of bounded operators to un- bounded operators on Hilbert space such as k-quasihyponormal and k-paranormal unbounded operators. Furthermore, we extend the Kaplansky theorem for normal…

The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…

In this paper we study operators originated from semi-B-Fredholm theory and as a consequence we get some results regarding boundaries and connected hulls of the corresponding spectra. In particular, we prove that a bounded linear operator…

In this article, we give a representation of $\ast$-paranormal absolutely norm attaining operator. Explicitly saying, every $\ast$-paranormal absolutely norm attaining ($\mathcal{AN}$ in short) $T$ can be decomposed as $U\oplus D$, where…

The pentablock, denoted as $\cP,$ is defined as follows: $$\cP= \left\{ (a_{21}, {\rm tr}(A), {\rm det}(A)) : A = [a_{ij}]_{2 \times 2} \text{ with } \|A\|<1 \right\}.$$ It originated from the work of Agler--Lykova--Young in connection with…

We consider norms on a complex separable Hilbert space such that $\langle a\xi,\xi\rangle\leq\|\xi\|^2\leq\langle b\xi,\xi\rangle$ for positive invertible operators $a$ and $b$ that differ by an operator in the Schatten class. We prove that…

Hyponormal operators are known to be among the most difficult operators to analyze. In this work, we focus on two finite types of hyponormal operators. The first type becomes analytic shifts, while the second type admits analytic models. A…