Related papers: Model Theory of a Hilbert Space Expanded with an U…

In this paper it is proved that each densely defined $J$-skew-symmetric operator (or each $J$-isometric operator with $\overline{D(A)}=\overline{R(A)}=H$) in a Hilbert space $H$ has a $J$-skew-self-adjoint (respectively $J$-unitary)…

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…

We study Heisenberg's matrix mechanics within an algebraic pre-Hilbert framework of arbitrary finite dimension. The commutator of the position and momentum matrices naturally generates a third Hermitian operator whose unbounded character…

In this work a possibility of a decomposition of a bounded operator which acts in a Hilbert space $H$ as a product of a J-unitary and a J-self-adjoint operators is studied, $J$ is a conjugation (an antilinear involution). Decompositions of…

Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…

We characterise the Kato property of a sectorial form $\mathfrak{a}$, defined on a Hilbert space $V$, with respect to a larger Hilbert space $H$ in terms of two bounded, selfadjoint operators $T$ and $Q$ determined by the imaginary part of…

Contractive selfadjoint extensions of a Hermitian contraction $B$ in a Hilbert space ${\mathfrak H}$ with an exit in some larger Hilbert space ${\mathfrak H}\oplus{\mathcal H}$ are investigated. This leads to a new geometric approach for…

Given a stationary continuous-time process $f(t)$, the Hilbert-Schmidt operator $A_{\tau}$ can be defined for every finite $\tau$\cite{Vautard1989SingularSA}. Let $\lambda_{\tau,i}$ be the eigenvalues of $A_{\tau}$ with descending order. In…

We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for such expansions to be unconditionally convergent in spaces with…

Let $H$ be a complex Hilbert space and let ${\mathcal C}$ be a conjugacy class of finite rank self-adjoint operators on $H$ with respect to the action of unitary operators. We suppose that ${\mathcal C}$ is formed by operators of rank $k$…

The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…

In resonance to a recent geometric framework proposed by Douglas and Yang, a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space is developed. By taking advantage of the refined…

We use a model operator approach and the spectral theorem for self-adjoint operators in a Hilbert space to derive the basic results of abstract left-definite theory in a straightforward manner. The theory is amply illustrated with a variety…

Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\sup\spec(A_0)\leq \inf\spec(A_1)$, where…

This monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator…

Let $ \Omega \subset \mathbb{C}^m $ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. Suppose that $\mathcal{M}_q$ is the quotient Hilbert module obtained from a…

We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain…

We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times…

Let M be a connected Riemannian manifold and let D be a Dirac type operator acting on smooth compactly supported sections in a Hermitian vector bundle over M. Suppose D has a self-adjoint extension A in the Hilbert space of…

We consider the massless Dirac operator with the MIT bag boundary conditions on an unbounded three-dimensional circular cone. For convex cones, we prove that this operator is self-adjoint defined on four-component $H^1$--functions…