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.

Let A be a C∗-algebra. Let E and F be Hilbert A-modules with E being full. Suppose that θ : E → F is a linear map preserving orthogonality, i.e., 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We show in this article that if, in addition, A has real rank zero, and θ is an A-module map (not assumed to be bounded), then there exists a central positive multiplier u ∈M(A) such that 〈θ(x), θ(y)〉 = u〈x, y〉 (x...

Given an arbitrary countable directed graph G we prove the C∗-envelope of the tensor algebra T+(G) coincides with the universal Cuntz-Krieger algebra associated with G. Our approach is concrete in nature and does not rely on Hilbert module machinery. We show how our results extend to the case of higher rank graphs, where an analogous result is obtained for the tensor algebra of a row-finite k-g...

Abstract. We prove that a conditionally completely positive definite kernel, as the generator of completely positive definite (CPD) semigroup associated with a continuous set of units for a product system over a C-algebra B, allows a construction of a Hilbert B−B module. That construction is used to define the index of the initial product system. It is proved that such definition is equivalent ...

We study the theory of a Hilbert space H as a module for a unital C∗-algebra A from the point of view of continuous logic. We show this theory, in an appropiate lenguage, has quantifier elimination and it is superstable. We show that for every v ∈ H the type tp(v/∅) is in correspondence with the positive linear functional over A defined by v. Finally, we characterize forking, orthogonality and ...

in this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of hilbert $c^ast-$ modules and vice versa, then we consider tensor products of g-bessel multipliers, bessel multipliers and bessel fusion multipliers in hilbert $c^ast-$modules. moreover, we obtain so...

Suppose that $${\mathscr {E}}$$ and {F}}$$ are Hilbert $$C^*$$ -modules. We present a power-norm $$\left( \left\| \cdot \right\| ^{{\mathscr {E}}}_n:n\in {\mathbb {N}}\right) $$ based on obtain some of its fundamental properties. introduce new definition the absolutely (2, 2)-summing operators from to , denote set such by $${\tilde{\Pi }}_2({\mathscr {E}},{\mathscr {F}})$$ with convention {E}})...

We introduce symmetrizing operators of the polynomial ring A[x] in the variable x over a ring A. When A is an algebra over a field k these operators are used to characterize the monic polynomials F (x) of degree n in A[x] such that A ⊗k k[x](x)/(F (x)) is a free A–module of rank n. We use the characterization to determine the Hilbert scheme parameterizing subschemes of length n of k[x](x). Intr...

In this paper, the special attention is given to the  product of two  modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented  that imply  the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved  that $P(RPQ)$ is idempotent, if $RPQ$†</...