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 agai...

this paper is concerned with a technique for solving volterra integral equations in the reproducing kernel hilbert space. in contrast with the conventional reproducing kernel method, the gram-schmidt process is omitted here and satisfactory results are obtained.the analytical solution is represented in the form of series.an iterative method is given to obtain the approximate solution.the conver...

In this article we study convexity properties of distance functions in infinite dimensional Finsler unitary groups, such as the full group, Schatten perturbations identity and groups finite von Neumann algebras. The structures are defined by translation different norms on tangent space at identity. We first prove a result for metric derived from operator norm group. also strong results squared ...

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

The spectral problem (A + V (z))ψ = zψ is considered with A, a self-adjoint operator. The perturbation V (z) is assumed to depend on the spectral parameter z as resolvent of another self-adjoint operator A ′ : V (z) = −B(A ′ − z) −1 B *. It is supposed that the operator B has a finite Hilbert-Schmidt norm and spectra of the operators A and A ′ are separated. Conditions are formulated when the p...