the paper deal with non-commutative geometry. the notion of quantumspheres was introduced by podles. here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

the aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von neumann algebra on a hilbert space with a normal faithful semi-finite trace $tau$. the submajorization inequalities generalize some results due to zhang, furuichi and lin, etc..

In this paper, we use soft linear operators to introduce the notion of discrete frames on Hilbert spaces, which extends classical spaces context algebraic structures sets. Among other results, show that frame operator associated a is bounded, self-adjoint, invertible and with bounded inverse. Furthermore, prove every element in space satisfies decomposition theorem. This theoretical framework p...

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space

in this paper we consider c0-group of unitary operators on a hilbert c*-module e. in particular we show that if a?l(e) be a c*-algebra including k(e) and ?t a c0-group of *-automorphisms on a, such that there is x?e with =1 and ?t (?x,x) = ?x,x t?r, then there is a c0-group ut of unitaries in l(e) such that ?t(a) = ut a ut*.

This paper introduces a temporal deductive database system featuring a logic programming language and an algebraic front-end. The language, called Temporal Datalog, is an extension of Datalog based on a simple temporal logic with two temporal operators, namely first and next. Programs of Temporal Datalog are considered as temporal deductive databases, specifying temporal relationships among dat...

In this paper we study the unitary equivalence between Hilbert modules over a locally C∗-algebra. Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally C∗-algebra and show that a Hilbert module over a Fréchet locally C∗-algebra is countably generated if and only if the locally C∗-algebra of all ”compact” operators has an approximate unit. 2000 Mathemat...

Labelled Deductive Systems provide a general method for representing logics in a modular and transparent way. A Labelled Deductive System consists of two parts, a base logic and a labelling algebra, which interact through a xed interface. The labelling algebra can be viewed as an independent parameter: the base logic stays xed for a given class of related logics from which we can generate the o...