In this paper, we introduce the concept of Q-P quantale modules. A series of categorical properties of Q-P quantale modules are studied, we prove that the category of Q-P quantale modules is not only pointed and connected, but also completed.

In the article, we find new dilatation results on non-commutative $$L^p$$ spaces. We prove that any self-adjoint, unital, positive measurable Schur multiplier some $$B(L^2(\Sigma ))$$ admits, for all $$1\leqslant p<\infty $$ , an invertible isometric dilation -space. obtain a similar result completely Fourier VN(G), when G is unimodular locally compact group. Furthermore, establish multivariabl...

The corona algebra M(A)/A contains essential information on the global structure of A, as demonstrated for instance by Busby theory. It is an interesting and surprisingly difficult task to determine the ideal structure of M(A)/A by means of the internal structure of A. Toward this end, we generalize Freudenthal’s classical theory of ends of topological spaces to a large class of C∗-algebras. Ho...

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior combine amplitude damping, inverse and pure dephasing. show mixing channels can result in restoring unitality, whereas commutative lead to non-commutativity. For Markovian semigroups, prove classical uncertainties cannot break quantum Markovianity. Moreover, contrary Pauli c...

A Leavitt labelled path algebra over a commutative unital ring is associated with space, generalizing algebras graphs and ultragraphs as well torsion-free generated by idempotents. We show that can be realized partial skew group rings, Steinberg algebras, Cuntz-Pimsner algebras. Via these realizations we obtain generalized uniqueness theorems, description of diagonal preserving isomorphisms cha...

and φA is the endomorphism induced on C(XA) by the one-sided subshift of finite type σA (see [6]) defined by (σAx)k = xk+1, x = (xk)k∈N ∈ XA. Therefore φA can be regarded as a non-commutative generalization of the one-sided subshift of finite type associated with the matrix A and the computation of its dynamical entropies is of some interest (see [4, Page 691]). When A(i, i) = 1, i ∈ Σ, one get...

This paper considers some extensions of the notion filter to quantale-valued context, including saturated prefilter, ?-filter and bounded prefilter. The question is whether these constructions give rise monads on category sets. It shown that answer depends structure quantale. Specifically, if quantale unit interval equipped with a continuous t-norm, then only implication operator corresponding ...

We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the qu...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...