In this paper, we show Hilbert C∗-module versions of Hölder– McCarthy inequality and its complementary inequality. As an application, we obtain Hölder type inequalities and its reverses on a Hilbert C∗-module.

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*.

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 $RPQ$†</...

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*.

We study a natural Hodge module on the Hilbert scheme of four points on affine three-space, which categorifies the Donaldson–Thomas invariant of the Hilbert scheme. We determine the weight filtration on the Hodge module explicitly in terms of intersection cohomology complexes, and compute the E-polynomial of its cohomology. The computations make essential use of a description of the singularity...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be again...

We show that the variational inequality $VI(C,A)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where$C$ is a nonempty closed convex subset of a Hilbert space $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

Frames on Hilbert C*-modules have been defined for unital C*algebras by Frank and Larson [5] and operator-valued frames on a Hilbert space have been studied in [8]. The goal of this paper is to introduce operatorvalued frames on a Hilbert C*-module for a σ-unital C*-algebra. Theorem 1.4 reformulates the definition given in [5] in terms of a series of rank-one operators converging in the strict ...