Related papers: Effects as functions on projective Hilbert space
We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By…
In this paper we determine a class of admissible matrices which are the Hilbert functions of some 0-dimensional schemes in $\mathbb P^1\times\mathbb P^1$.
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and…
For a Hilbert space H included in L^1_{loc} (R) of functions on $R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L^2(R) as well as our…
Quantum effects play an important role in quantum measurement theory. The set of all quantum effects can be organized into an algebraical structure called effect algebra. In this paper, we study various topologies on the Hilbert space…
A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.
We introduce a natural class of functions, the {\em pseudomultipliers}, associated with a general Hilbert function space, prove an extension theorem which justifies the definition, give numerous examples and establish the nature of the…
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful…
Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
Let X be a zero-dimensional scheme contained in a multiprojective space. Let $s_i$ be the length of the projection of X onto the i-th component of the multiprojective space. A result of Van Tuyl states that the Hilbert function of X, in the…
We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.
In this paper we introduce and study a new kind of generalized Hilbert matrix operators, induced by a positive finite Borel measure on (0,1), acting on weighted sequence spaces. We establish a sufficient and necessary condition for the…
In this paper, we study the generalized differentiability of the metric projection operator onto the positive cone in Hilbert spaces. We first establish the formula for exactly computing the regular coderivative and the Mordukhovich…
We prove that the set of orthogonal projections on a Hilbert space equipped with the length metric is $\frac\pi2$-geodesic. As an application, we consider the problem of variation of spectral subspaces for bounded linear self-adjoint…
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…
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained…
We study the functor l^2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and its homsets are algebraic domains; the latter category has conditionally algebraic domains…