Consider a Hilbert space obtained as the completion of the polynomials C[z ] in m-variables for which the monomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same is true for their restrictions to invariant subspaces spanned by monomials. This generalizes the result of Arveson [4] in which the Hilbert space is the m-shi...

In this paper we view some fundamentals of the theory of Hilbert C-modules and examine some ways in which Hilbert C-modules differ from Hilbert spaces. ∗2000 Mathematics Subject Classification. 46L08.

A Hilbert C∗-module is a generalisation of a Hilbert space for which the inner product takes its values in a C∗-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert C∗-modules over a group C∗-algebra which is generated by the group of translations associated with a wavelet. We shall investigate bracket products and their Fourier transform in the space of ...

Continuing the research on the Banach-Saks and Schur properties started in (cf. [10]) we investigate analogous properties in the module context. As an environment serves the class of Hilbert C∗-modules. Some properties of weak module topologies on Hilbert C∗-modules are described. Natural module analogues of the classical weak Banach-Saks and the classical Schur properties are defined and studi...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

Analogues for Hilbert C∗-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C∗-modules are studied with special attention paid on the differences with the well-known Hilbert space situation.

In this paper we introduce the curvature of densely defined universal connections on Hilbert C⁎-modules relative to a spectral triple (or unbounded Kasparov module), obtaining well-defined operator. Fixing triple, find that modulo junk forms, only depends represented form connection. We refine our definition factorizations modules. Our recovers all data Riemannian submersion compact manifolds, ...

some necessary and sufficient conditions are given for the existence of a g-positive (g-repositive) solution to adjointable operator equations $ax=c,axa^{left( astright) }=c$ and $axb=c$ over hilbert $c^{ast}$-modules, respectively. moreover, the expressions of these general g-positive (g-repositive) solutions are also derived. some of the findings of this paper extend some known results in the...

In this paper we introduce controlled *-g-frame and *-g-multipliers in Hilbert C*-modules and investigate the properties. We demonstrate that any controlled *-g-frame is equivalent to a *-g-frame and define multipliers for (C,C')- controlled*-g-frames .