Related papers: Some applications of the matched projections of id…
In this paper, we consider the CQ projection method and the shrinking projection method given by a finite family of nonexpansive mappings of the unit sphere of a real Hilbert space, and prove strong convergence theorems to common fixed…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
We define, for any special matching of a finite graded poset, an idempotent, regressive and order preserving function. We consider the monoid generated by such functions. The idempotents of this monoid are called special idempotents. They…
We construct some separable infinite dimensional homogeneous Hilbertian operator spaces which generalize the row and column spaces R and C. We show that separable infinite-dimensional Hilbertian JC*-triples are completely isometric to an…
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the…
We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…
We obtain the admissible sets on the unit circle to be the spectrum of a strict $m$-isometry on an $n$-finite dimensional Hilbert space. This property gives a better picture of the correct spectrum of an $m$-isometry. We determine that the…
This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…
A subalgebra $\mathcal{A}$ of $\mathbb{M}_n(\mathbb{C})$ is said to be projection compressible if $P\mathcal{A}P$ is an algebra for all orthogonal projections $P\in\mathbb{M}_n(\mathbb{C})$. Likewise, $\mathcal{A}$ is said to be idempotent…
We present commuting projection operators on de Rham sequences of two-dimensional multipatch spaces with local tensor-product parametrization and non-matching interfaces. Our construction yields projection operators which are local and…
Networks are structures that encode relationships between pairs of elements or nodes. However, there is no imposed connection between these relationships, i.e., the relationship between two nodes can be independent of every other one in the…
Let u be a hermitian involution, and e an orthogonal projection, acting on the same Hilbert space. We establish the exact formula, in terms of the norm of eue, for the distance from e to the set of all orthogonal projections q from the…
We show that a central linear mapping of a projectively embedded Euclidean $n$-space onto a projectively embedded Euclidean $m$-space is decomposable into a central projection followed by a similarity if, and only if, the least singular…
We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourer-finite-element-methods in weighted functions spaces. Closed Hilbert complexes and commuting projectors are used through…
Most research into similarity search in metric spaces relies upon the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common…
With this chapter we provide a compact yet complete survey of two most remarkable "representation theorems": every arguesian projective geometry is represented by an essentially unique vector space, and every arguesian Hilbert geometry is…
We establish new results concerning projectors on max-plus spaces, as well as separating half-spaces, and derive an explicit formula for the distance in Hilbert's projective metric between a point and a half-space over the max-plus…
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess…
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…