Related papers: Self-adjoint extensions with Friedrichs lower boun…

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…

In 2002, Littlejohn and Wellman developed a general left-definite theory for arbitrary self-adjoint operators in a Hilbert space that are bounded below by a positive constant. Zettl and Littlejohn, in 2005, applied this general theory to…

Given a densely defined skew-symmetric operators A 0 on a real or complex Hilbert space V , we parametrize all m-dissipative extensions in terms of contractions $\Phi$ : H-$\rightarrow$ H + , where Hand H + are Hilbert spaces associated…

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in…

In the terms of triples $D^+\to H\to D^-$ of Hilbert spaces we construct an analogue of Friedrichs's extension for operator matrices. Also we establish some general approach to construction of variational principles for such matrices.

We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model…

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…

For selfadjoint extensions tilde-A of a symmetric densely defined positive operator A_min, the lower boundedness problem is the question of whether tilde-A is lower bounded {\it if and only if} an associated operator T in abstract boundary…

We consider the formal prolate spheroid differential operator on a finite symmetric interval and describe all its self-adjoint boundary conditions. Only one of these boundary conditions corresponds to a self-adjoint differential operator…

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…

This note deals with the operator $T^*T$, where $T$ is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebesty\'en and Zs. Tarcsay [13]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed. In…

Here we give brief account of hermitian symplectic spaces, showing that they are intimately connected to symmetric as well as self-adjoint extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange…

The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…

Let $C$ be a conjugation on a Hilbert space $\mathcal{H}$. A densely defined linear operator $A$ on $\mathcal{H}$ is called $C$-symmetric if $CAC\subseteq A^*$ and $C$-self-adjoint if $CAC=A^*$. Our main results describe all…

Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator $S$ in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace ${\rm \overline{dom}\,} S$ are studied.…

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a…

For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the…

Given a finite set $X\subseteq\R$ we characterize the diagonals of self-adjoint operators with spectrum $X$. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to…

This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear…

We consider a linear symmetric operator in a Hilbert space that is neither bounded from above nor from below, admits a block decomposition corresponding to an orthogonal splitting of the Hilbert space and has a variational gap property…