in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

If the contraction T is a Toeplitz operator on H2 or A2 induced by an analytic function φ, we then denote the resulting space by H(φ). Similarly, if T is the Toeplitz operator on H2 or A2 induced by a conjugate analytic symbol φ, then we denote the resulting space by H(φ). In the context of Hardy spaces, H(φ) and H(φ) are called sub-Hardy Hilbert spaces by Sarason in [6]. We thus arrive at the ...

A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation p times we ...

Abstract. Certain facts about frames and generalized frames (g- frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. The paper also character- izes the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and suffcient condition is ob- ...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

The unitarizable modules in the analytic continuation of the holomorphic discrete series for tube type domains are realized as Hilbert spaces obtained through the Laplace transform.