Compact Quantum Systems and Norm Expansion with Observability of Conservative Systems

Abstract

The theory of multiplicity, mps was developed. A complete classification of right Coideal - algebras with a given parameter are obtained but the classification results for positive and negative cases of this parameter are different. Many of the Coideals are quantum spheres or quotient spaces by quantum subgroups. A process of orthogonal norm expansion along a subvariety of Co dimension 1 and dimension 2 on a weighted Bergman spaces over the Ball and the bidisk are introduced. We show various time discrtization schemes of abstract conservative evolution equations with askew- adjoint operator. We show that a pair of two operators is exactly observable for a continuous model.