Related papers: Adjoint Pairs and Unbounded Normal Operators

Let $T$ be an adjointable operator between two Hilbert $C^*$-modules and $T^*$ be the adjoint operator of $T$. The polar decomposition of $T$ is characterized as $T=U(T^*T)^\frac12$ and $\mathcal{R}(U^*)=\overline{\mathcal{R}(T^*)}$, where…

Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on…

An orthoset is a non-empty set $X$ together with a symmetric binary relation $\perp$ and a constant $0$ such that $x \not\perp x$ for any $x \neq 0$, and $0 \perp x$ for any $x$. Maps $f \colon X \to Y$ and $g \colon Y \to X$ between…

Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl--von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

This paper argues that non-self-adjoint operators can be observables. There are only four ways for this to occur: non-self-adjoint observables can either be normal operators, or be symmetric, or have a real spectrum, or have none of these…

We consider dissipative operators $A$ of the form $A=S+iV$, where both $S$ and $V\geq 0$ are assumed to be symmetric but neither of them needs to be (essentially) selfadjoint. After a brief discussion of the relation of the operators $S\pm…

In the present paper we give results on the closedness and the self-adjointness of the sum of two unbounded operators. We present a new approach to these fundamental questions in operator theory. We also prove a new version of the Fuglede…

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan…

The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…

Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…

For $0<r<1$, let us consider the following annulus: \[ \mathbb A_r= \{ z\in \mathbb C\, : \, r<|z|<1 \}. \] A Hilbert space operator $T$ for which $\overline{\mathbb A}_r$ is a spectral set is called an $\mathbb A_r$-\textit{contraction}.…

In this work, in the Hilbert space of vector-functions L^2 (H,(-\infty,a)\cup(b,+\infty)),a<b all normal extensions of the minimal operator generated by linear singular formally normal differential expression l(\cdot)=(d/dt+A_1,d/dt+A_2)…

This paper investigates quasi-selfadjoint extensions of dual pairs of linear relations in Hilbert spaces. Some properties of dual pairs of linear relations are given and an Hermitian linear relation associated with a dual pair of linear…

In this paper, we characterize absolute norm-attainability for compact hyponormal operators. We give necessary and sufficient conditions for a bounded linear compact hyponormal operator on an infinite dimensional complex Hilbert space to be…

In this paper we study Birkhoff-James Orthogonality for biadjoints of operators. We partly solve the problem, if an operator is orthogonal to the space of operators valued in a subspace, when the is the norm of biadjoint is attained at a…

In this paper, we establish several characterizations of the $A$-parallelism of bounded linear operators with respect to the seminorm induced by a positive operator $A$ acting on a complex Hilbert space. Among other things, we investigate…

We consider an abstract sequence $\{A_n\}_{n=1}^\infty$ of closed symmetric operators on a separable Hilbert space $\mathcal{H}$. It is assumed that all $A_n$'s have equal deficiency indices $(k,k)$ and thus self-adjoint extensions…

Let $\mathcal{B}(H)$ be the bounded, linear operators on a separable Hilbert space equipped with the norm topology. A property is called typical if the set of operators fulfilling the property is co-meager. We show that having non-empty…

Let $\mathcal{H}$ be a separable complex Hilbert space. A conjugate-linear map $C:\mathcal{H}\to \mathcal{H}$ is called a conjugation if it is an involutive isometry. In this paper, we focus on the following interpolation problems: Let…