The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

This paper presents a framework for plot control in interactive story systems. In this framework, the user takes the place of the main character of the story, the protagonist. The rest of the cast consists of discrete characters, each playing a specific role in the story. A separate module in this system, the plot manager, controls the behavior of the cast and specifies what the protagonist can...

In the first part of paper, we use states on $C^*$-algebras in order to establish some equivalent statements equality triangle inequality, as well parallelogram identity for elements a pre-Hilbert $C^*$-module. We also characterize case inequality adjointable operators Hilbert Then give certain necessary and sufficient conditions Pythagoras two vectors $C^*$-module under assumption that their i...

Let M be a space of weakly*-measurable functions F : ? B(H) on measure (?,?,?), for which the function F*F is Gel'fand integrable and integral d? nuclear operator Hilbert H. We show that H*-module contains an orthonormal basis.

Let E and F be two Hilbert C∗-modules over C∗-algebras A and B, respectively. Let T be a surjective linear isometry from E onto F and φ a map from A into B. We will prove in this paper that if the C∗-algebras A and B are commutative, then T preserves the inner products and T is a module map, i.e., there exists a ∗-isomorphism φ between the C∗-algebras such that 〈Tx, Ty〉 = φ(〈x, y〉), and T (xa) ...