The principal result of this paper states that if X is a pre-Hilbert B-module over an arbitrary C*-
algebra B, then the B-valued inner product on X can be lifted to a B-valued inner product on …

This paper is an investigation of right modules over a ${B^\ast} $-algebra B which posses a
B-valued “inner product” respecting the module action. Elementary properties of these …

We regard a right Hilbert C*-module X over a C*-algebra A endowed with an isometric*-
homomorphism\phi: A\to L_A (X) as an object X_A of the C*-category of right Hilbert A …

Let $ A $, $ B $ be $ C^* $-algebras and $ E $ a full Hilbert $ A $-$ B $-bimodule such that
every closed right submodule $ E_ {0}\subseteq E $ is orthogonally closed, ie, $ E_ {0}=(E …

We extend Sakai's characterization of von Neumann algebras to the context of Hilbert C*-
modules. If A, B are C*-algebras and X is a full Hilbert AB-bimodule possessing a predual …

Let A be a C∗-algebra and X a Banach A-module. The module action of A on X gives rise to
module actions of A∗∗ on X∗ and X∗∗, and derivations of A into X (resp. X∗) extend to …

This paper considers Hilbert C*-bimodules, a slight generalization of imprimitivity bimodules
which were introduced by Rieffel [20]. Brown, Green, and Rieffel [7] showed that every …

One difference between Hilbert modules and Hilbert spaces is that Hilbert modules are not
“self-dual” in general. Another difference is that Hilbert modules are not orthogonally …

HILBERT C ∗−MODULES IN WHICH ALL CLOSED SUBMODULES ARE COMPLEMENTED
1. Introduction and the main result It is well known tha Page 1 PROCEEDINGS OF THE …

The main result asserts that given two monotone complete C*-algebras A and B, B is
faithfully represented as a monotone closed C*-subalgebra of the monotone complete C …