. O A ] 1 2 Ju n 19 99 MODULES OVER OPERATOR ALGEBRAS , AND THE MAXIMAL C ∗ − DILATION
نویسنده
چکیده
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 technology is quite general, however it was developed to solve some problems arising in the theory of Morita equivalence of operator algebras, and as a result most of the applications given here (and in a companion paper) are to that subject. Other applications given here are to extension problems for module maps, and characterizations of C∗−algebras. * Supported by a grant from the NSF. The contents of this paper were announced at the January 1999 meeting of the American Mathematical Socety.
منابع مشابه
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...
متن کاملSome Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras
In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...
متن کاملA Morita Theorem for Dual Operator Algebras
We prove that two dual operator algebras are weak Morita equivalent in the sense of [4] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weakcontinuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case we can characterize such functors as the module normal Haagerup tensor product ...
متن کامل*-frames in Hilbert modules over pro-C*-algebras
In this paper, by using the sequence of multipliers, we introduce frames with algebraic bounds in Hilbert pro-$ C^* $-modules. We investigate the relations between frames and $ ast $-frames. Some properties of $ ast $-frames in Hilbert pro-$ C^* $-modules are studied. Also, we show that there exist two differences between $ ast $-frames in Hilbert pro-$ C^* $-modules and Hilbert $ ...
متن کاملar X iv : m at h / 04 07 22 0 v 1 [ m at h . O A ] 1 3 Ju l 2 00 4 DUALITY AND OPERATOR ALGEBRAS
We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always w *-continuous on dual operator spaces. For example, this yields a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999