Related papers: Oblique projections on metric spaces

We characterize the sets of norm one vectors $\mathbf{x}_1,\ldots,\mathbf{x}_k$ in a Hilbert space $\mathcal H$ such that there exists a $k$-linear symmetric form attaining its norm at $(\textbf{x}_1,\ldots,\mathbf{x}_k)$. We prove that in…

We give an inequality on the packing of vectors/lines in quaternionic Hilbert space $\Hd$, which generalises those of Sidelnikov and Welch for unit vectors in $\Rd$ and $\Cd$. This has a parameter $t$, and depends only on the vectors up to…

The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator $ A $ on a Hilbert space $ \mathbb{H}, $ we define $ (\epsilon,A)- $approximate…

We prove a functional identity between the Hilbert metric and the visual angle metric in the unit disk. The proof utilizes the Poincar\'e hyperbolic metric in terms of which both metrics can be expressed. This identity then yields sharp…

We give new inequalities for $A$-operator seminorm and $A$-numerical radius of semi-Hilbertian space operators and show that the inequalities obtained here generalize and improve on the existing ones. Considering a complex Hilbert space…

Semi-cosimplicial objects in the category of Hilbert spaces with isometries which are motivated by non-commutative probability theory, in particular by the distributional symmetry of spreadability, are introduced and systematically…

The problem of the determination of the Hilbert-space metric which renders a given Hamiltonian $H$ self-adjoint is addressed from the point of view of applicability of computer-assisted algebraic manipulations. An exactly solvable example…

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 study approximation properties of weighted $\mathrm{L}^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the reflection-invariant form $(1-\lVert x \rVert^2)^\alpha…

We develop a Heisenberg-picture \emph{kinematical} framework in which (i) time is treated as a quantum observable, admitting both a relational POVM construction for semibounded spectra and a fully self-adjoint realization on an enlarged…

Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…

We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized…

The gravitational path integral suggests a striking result: the Hilbert space of closed universes in each superselection sector, a so-called $\alpha$-sector, is one-dimensional. We develop an abstract formalism encapsulating recent…

A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator $T$ on a Hilbert space $\mathcal{H}$ is a perturbation of a selfadjoint operator, and the spectral…

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2…

In this paper we study the following hypergeometric polynomials: $\mathcal{P}_n(x) = \mathcal{P}_n(x;\alpha,\beta,\delta_1,\dots,\delta_\rho,\kappa_1,\dots,\kappa_\rho) = {}_{\rho+2} F_{\rho+1}…

Frames on Hilbert C*-modules have been defined for unital C*-algebras by Frank and Larson and operator valued frames on a Hilbert space have been studied in arXiv.0707.3272v1.[math.FA]. Goal of the present paper is to introduce operator…

Commutative Hilbertian Frobenius algebras are those commutative semi-group objects in the monoidal category of Hilbert spaces, for which the Hilbert adjoint of the multiplication satisfies the Frobenius compatibility relation, that is, this…

In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…