Related papers: Chernoff Like Counterexamples Related to Unbounded…

We construct operators which factorize the transfer function associated with a non-self-adjoint 2x2 operator matrix whose diagonal entries can have overlapping spectra and whose off-diagonal entries are unbounded operators.

We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of…

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

We give a precise and complete description on the spectrum for a class of non-self-adjoint quasi-periodic operators acting on $\ell^2(\mathbb{Z}^d)$ which contains the Sarnak's model as a special case. As a consequence, one can see various…

In [9] a question is raised: if a power bounded operator is quasisimilar to a singular unitary operator, is it similar to this unitary operator? For polynomially bounded operators, a positive answer to this question is known [1], [13]. In…

In this paper we consider the order-like relation for self-adjoint operators on some Hilbert space. This relation is defined by using Jensen inequality. We will show that under some assumptions this relation is antisymmetric.

The eigenvalues of a self-adjoint nxn matrix A can be put into a decreasing sequence $\lambda=(\lambda_1,...,\lambda_n)$, with repetitions according to multiplicity, and the diagonal of A is a point of $R^n$ that bears some relation to…

In this note self-adjoint extensions of symmetric operators are investigated by using the abstract technique of quasi boundary triples and their Weyl functions. The main result is an extension of Theorem 2.6 in [5] which provides sufficient…

In this paper, necessary and sufficient conditions are established for the factorization of a closed, in general, unbounded operator $T=AB$ into a product of two nonnegative selfadjoint operators $A$ and $B.$ Already the special case, where…

For self-adjoint operators $A, B$, a bounded operator $J$, and a function $f:\mathbb R\to\mathbb C$ we obtain bounds in quasi-normed ideals of compact operators for the difference $f(A)J-Jf(B)$ in terms of the operator $AJ-JB$. The focus is…

This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is…

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…

We construct in this article a class of closed semi-bounded quadratic forms on the space of square integrable functions over a smooth Riemannian manifold with smooth boundary. Each of these quadratic forms specifies a semi-bounded…

Using the concept of intrinsic metric on a locally finite weighted graph, we give sufficient conditions for the magnetic Schr\"odinger operator to be essentially self-adjoint. The present paper is an extension of some recent results proven…

Let $M$ be a complete Riemannian manifold and let $\Omega^*(M)$ denote the space of differential forms on $M$. Let $d:\Omega^*(M) \to \Omega^{*+1}(M)$ be the exterior differential operator and let $\Del=dd^*+d^*d$ be the Laplacian. We…

The main goal of this paper is to show that a (not necessarily densely defined or closed) symmetric operator $A$ acting on a real or complex Hilbert space is selfadjoint exactly when $I+A^2$ is a full range operator.

The primary purpose of the present paper is to investigate when relations of the types $|AB|=|A||B|$, $|A\pm B|\leq |A|+|B|$, $||A|-|B||\leq |A\pm B|$ and $|\overline{\text{Re} A}|\leq |A|$ (among others) hold in an unbounded operator…

We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular…

We are interested in an open question raised by Fong-Tsui (dating back to the beginning of the eighties of last century) as to whether a bounded operator whose absolute value is less than the absolute value of its real part is self-adjoint.…

We prove that some non-self-adjoint differential operator admits factorization and apply this new representation of the operator to construct explicitly its domain. We also show that this operator is J-self-adjoint in some Krein space.