Related papers: Extensions of symmetric operators I: The inner cha…

We give an explicit description of all minimal self-adjoint extensions of a densely defined, closed symmetric operator in a Hilbert space with deficiency indices $(1, 1)$.

We revise Krein's extension theory of positive symmetric operators. Our approach using factorization through an auxiliary Hilbert space has several advantages: it can be applied to non-densely defined transformations and it works in both…

It is shown that a contraction on a Hilbert space is complex symmetric if and only if the values of its characteristic function are all symmetric with respect to a fixed conjugation. Applications are given to the description of complex…

In this work, firstly in the Hilbert space of vector-functions L^2 (H,(-\infty,a)\bup(b,+\infty)),a<b all selfadjoint extensions of the minimal operator generated by linear singular symmetric differential expression l(\cdot)=i d/dt+A with a…

We produce a simple criterion and a constructive recipe to identify those self-adjoint extensions of a lower semi-bounded symmetric operator on Hilbert space which have the same lower bound as the Friedrichs extension. Applications of this…

Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…

An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove…

In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…

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…

In a real Hilbert spaces H a smooth operator F is studied, whose derivative at each point of its domain is a symmetric operator. In terms of abstract boundary conditions locally self-adjoint extensions of this operator are described. We use…

Let $A_\N$ be the symmetric operator given by the restriction of $A$ to $\N$, where $A$ is a self-adjoint operator on the Hilbert space $\H$ and $\N$ is a linear dense set which is closed with respect to the graph norm on $D(A)$, the…

A densely-defined symmetric linear map from/to a real Hilbert space extends to a self-adjoint map. Extension is expressed via Riesz representation. For a case including Friedrichs extension of a strongly monotone map, self-adjoint extension…

This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory…

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)…

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…

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…

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 $S$ be a symmetric operator with equal defect numbers and let $\mathfrak{U}$ be a set of unitary operators in a Hilbert space $\mathfrak{H}$. The operator $S$ is called $\mathfrak{U}$-invariant if $US=SU$ for all $U\in\mathfrak{U}$.…

Let $A = (A_1, \ldots, A_n)$ and $B = (B_1, \ldots, B_n)$ be row contractions on $\mathcal{H}_1$ and $\mathcal{H}_2$, respectively, and $X$ be a row operator from $\oplus_{i=1}^n \mathcal{H}_2$ to $\mathcal{H}_1$. Let $D_{A^*} = (I - A…

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.…