Related papers: Hilbert space operators with compatible off-diagon…

Let ${\mathbb B}(\mathscr H)$ denote the set of all bounded linear operators on a complex Hilbert space ${\mathscr H}$. In this paper, we present some norm inequalities for sums of operators which are a generalization of some recent…

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…

An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the infinite-dimensional Hubbard model is developed on the basis of a…

Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is,…

Let $H(\mathbb{D})$ be the space of all analytic functions in the unit disc $\mathbb{D}$. For $g\in H(\mathbb{D})$, the generalized Hilbert operator $\mathcal{H}_{g}$ is defined by $$\mathcal{H}_{g}(f)(z)=\int_{0}^{1}f(t)g'(tz)dt, \ \ z\in…

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

Let T be a quasidiagonal operator on a separable Hilbert space. Then T is the norm limit of operators, each of which generate a finite dimensional C*-algebra, if and only if the C*-algebra generated by T is exact.

We establish a new decomposition formula for two orthogonal projections P and Q on a separable Hilbert space V. This formula yields an orthogonal direct sum decomposition of V into invariant subspaces under P and Q, each of which is either…

For a bounded quaternionic operator $T$ on a right quaternionic Hilbert space $\mathcal{H}$ and $\varepsilon >0$, the pseudo $S$-spectrum of $T$ is defined as \begin{align*} \Lambda_{\varepsilon}^{S}(T) := \sigma_S (T) \bigcup \left \{ q…

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…

Let $T\in\mathbb{B}(\mathscr{H})$ and $T=U|T|$ be its polar decomposition. We proved that (i) if $T$ is log-hyponormal or $p$-hyponormal and $U^n=U^\ast$ for some $n$, then $T$ is normal; (ii) if the spectrum of $U$ is contained in some…

Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…

Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates…

A bounded linear operator $A$ on a Hilbert space $\mathcal{H}$ is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. We show that if $A$ is posinormal with closed range, then $A^n$ is posinormal and has closed…

In this paper we introduce and prove some properties of $(\alpha;\beta)$-normal operators according to semi-Hilbertian space structures. Furthermore we s,ate various inequalities between the A-operator norm and A-numerical radius of…

If $\mathcal H$ is a Hilbert space, $\mathcal S \subseteq \mathcal H$ is a closed subspace of $\mathcal H$, and $A $ is a positive bounded linear operator on $\mathcal H$, the spectral shorted operator $\rho(\mathcal S, A)$ is defined as…

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…

In this paper, the concept of Birkhoff--James orthogonality of operators on a Hilbert space is generalized when a semi-inner product is considered. More precisely, for linear operators $T$ and $S$ on a complex Hilbert space $\mathcal{H}$, a…

A polygon is derived that contains the numerical range of a bounded linear operator on a complex Hilbert space, using only norms. In its most general form, the polygon is an octagon, symmetric with respect to the origin, and tangent to the…