Gleason's theorem in a space with indefinite metric

An analog to the Gleason theorem for measures on logics of projections in indefinite metric spaces is proved

Measure on the inductive limit of projection lattices

A probability measure on a nondecreasing net of lattices of orthogonal projections in von Neumann algebras is extended to a probability on the inductive limit of the lattices. © 1993 Plenum Publishing Corporation

Vitali-Hahn-Saks theorem for hyperbolic logics

An analog to the Vitali-Hahn-Saks theorem for indefinite measures on hyperbolic logics of projections in indefinite metric spaces is proved. © 1995 Plenum Publishing Corporation

Skew-symmetric functions on the hyperboloid and quantum measures

Measures on the logic of J-projections on an indefinite metric space of dimension two are studied

Any Regular Measure on Conjugation Logic is a Complex Measure

Let H be the complex Hilbert space with conjugation J. Denote by B(H)co the quantum logic of all J-projections on H. A non-zero function μ({dot operator}):=tr(A({dot operator})) on B(H)co is said to be a regular measure. Here A is a trace class operator. It is shown that there exists a J-projection p such that. We give a description of the hermitian and skew hermitian regular measures. © 2011 Springer Science+Business Media, LLC

Von Neumann algebras and projections in space with conjugation operator

In the paper we give a classification of von Neumann algebras in Hilbert space with conjugation operator and we study J-projections from von Neumann J-algebras of type (B) for the first time. © 2014 Pleiades Publishing, Ltd

Idempotents as J-projections: II

Let B(H) Id be the set of all bounded idempotents on a complex Hilbert space H and let J be a conjugation operator on H. Fix p ∈ B(H) Id. At the paper we describe of J-projections. We prove that for a given p there exists a conjugation operator J 0 such that p is a J 0-projection. © 2012 Pleiades Publishing, Ltd

Idempotents in a space with conjugation

Let H be a complex Hilbert space with conjugation operator J. We study J-real operators and we have covered J-regular subspaces. We prove that for given bounded idempotent p there exists a conjugation operator J0 such that p is a J0-projection, i.e. p= J0p J0. © 2012 Elsevier Inc. All rights reserved

Semiconstant measures on hyperbolic logics

We characterize the set of all semiconstant measures on the hyperbolic logics of projections in indefinite metric spaces and describe the set of all probability measures on these logics. ©1997 American Mathematical Society

Idempotents and Krein space

Let B(H)Id be the set of all bounded idempotents on a Hilbert space H. Fix p ∈ B(H)Id. The aim of the paper is to show a set of symmetries J on H for which p is a J-projection. © 2011 Pleiades Publishing, Ltd