Modules over Operator Algebras, and the Maximal C*-Dilation

. O A ] 1 2 Ju n 19 99 MODULES OVER OPERATOR ALGEBRAS , AND THE MAXIMAL C ∗ − DILATION

We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect ‘nonselfadjoint operator algebra’ with the C∗−algebraic framework. More particularly, we make use of the universal, or maximal, C∗−algebra generated by an operator algebra, and C∗−dilations. This technolog...

Hilbert modules over pro-C*-algebras

In this paper, we generalize some results from Hilbert C*-modules to pro-C*-algebra case. We also give a new proof of the known result that l2(A) is aHilbert module over a pro-C*-algebra A.

Characterizations of Essential Ideals as Operator Modules over C*-algebras

In this paper we give characterizations of essential left ideals of a C*-algebra A in terms of their properties as operator A-modules. Conversely, we seek C*-algebraic characterizations of those ideals J in A such that A is an essential extension of J in various categories of operator modules. In the case of two-sided ideals, we prove that all the above concepts coincide. We obtain results, ana...

G-frames in Hilbert Modules Over Pro-C*-‎algebras

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...

Fusion frames in Hilbert modules over pro-C*-algebras