Hilbert C∗-modules are useful tools in AW ∗-algebra theory, theory of operator algbras, operator K-theory, group representation theory and theory of operator spaces. The theory of Hilbert C∗-modules is very interesting on its own. In this paper we give fundamentals of the theory of Hilbert C∗-modules and examine some ways in which Hilbert C∗-modules differ from Hilbert spaces.

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

In this paper, we introduce the concepts of $ast$-K-g-Frames in Hilbert $mathcal{A}$-modules and we establish some results.

In this paper, we investigate the mapping of continuous g-frames in Hilbert C*-module under bounded operators. So, operators that preserve continuous g-frames in Hilbert C*-module were characterized. Then, we introduce equivalent continuous g-frames in Hilbert C*-module by the mapping of continuous g-frames in Hilbert C*-module under bounded operators. We show that every continuous g-frame in H...

Contents 1 Conventions and basic notation 2 2 Hilbert variety: the general framework 3 3 The Hilbert curve 8 4 Cubic Hilbert curves 12 5 Image of the Hilbert curve in P 3 17 6 Fibrations and singular points of the Hilbert curve at infinity 19 7 Serre-invariant curves 23 Abstract Let X be a normal Gorenstein complex projective variety. We introduce the Hilbert variety V X associated to the Hilbe...

Let V ⊗HS W be the completion of V ⊗alg W in the norm defined by this inner product. V ⊗HS W is a Hilbert space; however, as Garrett shows it is not a categorical tensor product, and in fact if V and W are Hilbert spaces there is no Hilbert space that is their categorical tensor product. (We use the subscript HS because soon we will show that V ⊗HS W is isomorphic as a Hilbert space to the Hilb...

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...