Riesz bases and positive operators on Hilbert space.
Roots of positive and negative operators on Wachs spaces
Sampling of Band-Limited Vectors.
Sesquilinear and Quadratic Forms on Modules Over *-algebras
Sesquilinear-orthogonally quadratic mappings.
Sets invariant under projections onto two dimensional subspaces
The Blaschke–Kakutani result characterizes inner product spaces , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace there is a norm 1 linear projection onto . In this paper, we determine which closed neighborhoods of zero in a real locally convex space of dimension at least 3 have the property that for every 2 dimensional subspace there is a continuous linear projection onto with .
Shapes and computer generation of numerical ranges of Krein space operators.
Signed states on a logic
Sobre relativización de convergencias en G(H).
Given a real separable Hilbert space H, G(H) denotes the Geometry of the closed linear subspaces of H, S = {E(n) | n belonging to N} a sequence of G(H) and [E] the closed linear hull of E. The weak, strong and other convergences in G(H) were defined and characterized in previous papers. Now we study the convergence of sequences {E(n) ∩ F | n belonging to N} when {E(n)} is a convergent sequence and F is a subspace of G(H), and we show that these convergences hold, if this intersection exists. Conversely,...
Solving moment problems by dimensional extension.
Some Boas-Bellman type inequalities in 2-inner product spaces.
Some characteristic and non-characteristic properties of inner product spaces
Some characterization of locally nonconical convex sets
A closed convex set in a local convex topological Hausdorff spaces is called locally nonconical (LNC) if for every there exists an open neighbourhood of such that . A set is local cylindric (LC) if for , , there exists an open neighbourhood of such that (equivalently: ) is a union of open segments parallel to . In this paper we prove that these two notions are equivalent. The properties LNC and LC were investigated in [3], where the implication was proved in general, while...
Some companions of the Grüss inequality in inner product spaces.
Some existence results on noncoercive variational inequalities
Some generalization of Steinhaus' lattice points problem
Steinhaus' lattice points problem addresses the question of whether it is possible to cover exactly n lattice points on the plane with an open ball for every fixed nonnegative integer n. This paper includes a theorem which can be used to solve the general problem of covering elements of so-called quasi-finite sets in Hilbert spaces. Some applications of this theorem are considered.
Some geometric properties of typical compact convex sets in Hilbert spaces
An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection from e to X has fixed cardinality n+1 ( arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection from e to X where X is a compact subset of .
Some Grüss type inequalities in inner product spaces.
Some inequalities in functional analysis, combinatorics, and probability theory.
Some more weak Hubert spaces
We construct, by a variation of the method used to construct the Tsirelson spaces, a new family of weak Hilbert spaces which contain copies of l₂ inside every subspace.