Related papers: Selfadjoint Extensions of a Singular Multipoint Di…

Let $\Omega_-$ and $\Omega_+$ be two bounded smooth domains in $\mathbb{R}^n$, $n\ge 2$, separated by a hypersurface $\Sigma$. For $\mu>0$, consider the function $h_\mu=1_{\Omega_-}-\mu 1_{\Omega_+}$. We discuss self-adjoint realizations of…

We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$…

We investigate the Hardy space $H^1_L$ associated with a self-adjoint operator $L$ defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates,…

For an unbounded self-adjoint operator D on a Hilbert space H and a bounded operator a on H we say that a is weakly D-differentiable if for any pair of vectors x, y in H the function <exp(itD) a exp(-itD)x, y> is differentiable at t =0. We…

We define the (convex) joint numerical range for an infinite family of compact operators in a Hilbert space H. We use this set to determine whether a self-adjoint compact operator A with {||A||, -||A||} in its spectrum is minimal respect to…

Let $J,E\subset\mathbb R$ be two multi-intervals with non-intersecting interiors. Consider the following operator $$A:\, L^2( J )\to L^2(E),\ (Af)(x) = \frac 1\pi\int_{ J } \frac {f(y)\text{d} y}{x-y},$$ and let $A^\dagger$ be its adjoint.…

In this paper we study invertible extensions of a symmetric operator in a Hilbert space $H$. All such extensions are characterized by a parameter in the generalized Neumann's formulas. Generalized resolvents, which are generated by the…

This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…

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…

Given a self-adjoint operator $H\geq 0$ and (appropriate) densely defined and closed operators $P_{1},\dots, P_{n}$ in a Hilbert space $\mathscr{H}$, we provide a systematic study of bounded operators given by iterated integrals…

In this paper, we shall characterize the components of the polar decomposition for an arbitrary $J$-unitary operator in a Hilbert space. This characterization has a quite different structure as that for complex symmetric and complex…

We consider an off-diagonal self-adjoint finite rank perturbation of a self-adjoint operator in a complex separable Hilbert space $\mathfrak{H}_0 \oplus \mathfrak{H}_1$, where $\mathfrak{H}_1$ is finite dimensional. We describe the singular…

This paper delves into several characterizations of $A$-approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space $H$ and also investigates properties of the $A$-approximate point spectrum for the tensor…

Distinguished selfadjoint extensions of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, $-|x|^{-1}$. The method uses Hardy-Dirac inequalities and quadratic form techniques.

In the present paper we investigate the set $\Sigma_J$ of all $J$-self-adjoint extensions of a symmetric operator $S$ with deficiency indices $<2,2>$ which commutes with a non-trivial fundamental symmetry $J$ of a Krein space…

Let ${\mathsf D}$ and ${\mathsf H}$ be the self-adjoint, one-dimensional Dirac and Schr\"odinger operators in $L^{2}(\mathbb{R};\mathbb{C}^{2})$ and $L^{2}(\mathbb{R};\mathbb{C})$ respectively. It is well known that, in absence of an…

Let $\dot A$ be a densely defined, closed, symmetric operator in the complex, separable Hilbert space $\mathcal{H}$ with equal deficiency indices and denote by $\mathcal{N}_i = \ker \big(\big(\dot A\big)^* - i I_{\mathcal{H}}\big)$, $\dim…

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…

We relate non integer powers ${\mathcal L}^{s}$, $s>0$ of a given (unbounded) positive self-adjoint operator $\mathcal L$ in a real separable Hilbert space $\mathcal H$ with a certain differential operator of order $2\lceil{s}\rceil$,…

Given two linear operators $S$ and $T$ acting between Hilbert spaces $\mathscr{H}$ and $\mathscr{K}$, respectively $\mathscr{K}$ and $\mathscr{H}$ which satisfy the relation \begin{equation*} \langle Sh, k\rangle=\langle h, Tk\rangle, \quad…