Related papers: Dichotomy between operators acting on finite and i…
We investigate elliptic boundary-value problems for which the maximum of the orders of the boundary operators is equal to or greater than the order of the elliptic differential equation. We prove that the operator corresponding to an…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
The finite entropy of black holes suggests that local regions of spacetime are described by finite-dimensional factors of Hilbert space, in contrast with the infinite-dimensional Hilbert spaces of quantum field theory. With this in mind, we…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and different from an end as a metric space. Such an indexed…
In this paper we study Volterra type operators on infinite dimensional simplex. It is provided a sufficient condition for Volterra type operators to be bijective. Furthermore it is shoved that the condition is not necessary.
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm…
We compare and contrast results of E. Davis, of A. Bigatti, A.V. Geramita and the author, and of J. Ahn and the author. The underlying idea is that certain numerical conditions on the Hilbert function of a finite set of points in projective…
The description of all correct restrictions of the maximal operator are considered in a Hilbert space. A class of correct restrictions are obtained for which a similar transformation has the domain of the fixed correct restriction. The…
In this paper, we present some interesting results to characterize the Moore-Penrose inverses of unbounded closable operators and the Cartesian product of closed operators in Hilbert spaces.
An operator $T$ acting on a Hilbert space is called $(\alpha ,\beta)$-normal ($0\leq \alpha \leq 1\leq \beta $) if \begin{equation*} \alpha ^{2}T^{\ast }T\leq TT^{\ast}\leq \beta ^{2}T^{\ast}T. \end{equation*} In this paper we establish…
The aim of this work is to study the structure of bounded finite potent endomorphisms on Hilbert spaces. In particular, for these operators, an answer to the Invariant Subspace Problem is given and the main properties of its adjoint…
Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially…
We give an iteration scheme for finding zeros of maximal monotone operators in Hilbert spaces. We assume that the operator is defined in the whole space. The iterates converge strongly to a solution if there exists any, otherwise they tend…
We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…
In this paper, we further investigate the problem of commutativity up to a factor (or $\lambda$-commutativity) in the setting of bounded and unbounded linear operators in a complex Hilbert space. The results are based on a new approach to…
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
The aim of this article is to define and compare several distances (or metrics) between operators acting on different (separable) Hilbert spaces. We consider here three main cases of how to measure the distance between two bounded…