On Quantum Itô Algebras and Their Decompositions

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Subdirect Decompositions of Lattice Effect Algebras

We prove a theorem about subdirect decompositions of lattice effect algebras. Further, we show how, under these decompositions, blocks, sets of sharp elements and centers of those effect algebras are decomposed. As an application we prove a statement about the existence of subadditive state on some block-finite effect algebras.

The Role of Type III Factors in Quantum Field Theory

One of von Neumann’s motivations for developing the theory of operator algebras and his and Murray’s 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite number of degrees of freedom the simplest possibility, i.e., factors of type I in the terminology of Murray and von Neumann, are perfectly adequ...

The witness set of coexistence of quantum effects and its preservers

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

A ] 2 1 Ju l 2 00 3 Representations of cross product algebras of Podleś quantum spheres

Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podleś spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf...