What is a Hilbert C ∗-module? ∗

نویسندگان

  • Mohammad Sal Moslehian
  • M. A. Rieffel
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Frames in super Hilbert modules

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.

متن کامل

$G$-dual Frames in Hilbert $C^{*}$-module Spaces

In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

متن کامل

Arens regularity and derivations of Hilbert modules with the certain product

Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$  is Arens regular. We also study the relationship between derivations of $A$ and $E$.

متن کامل

On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

متن کامل

Approximately higher Hilbert $C^*$-module derivations

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

متن کامل

Dilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002