NEW EXAMPLES OF CONTINUOUS SPATIAL SEMIGROUPS OF *-ENDOMORPHISMS OF ${\mathfrak B} ({\mathfrak h})$

DOI10.1142/S0129167X99000094zbMath0973.46051OpenAlexW2277113715MaRDI QIDQ4518292

Robert T. Powers

Publication date: 20 November 2001

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x99000094

zbMATH Keywords

\(E_0\)-semigroups\(*\)-endomorphismsArveson indexCAR-CCR flows

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Linear symmetric and selfadjoint operators (unbounded) (47B25) States of selfadjoint operator algebras (46L30) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (20)

On the product system of a completely positive semigroup ⋮ Examples of multiparameter CCR flows with non-trivial index ⋮ The index of a quantum dynamical semigroup ⋮ Roots of completely positive maps ⋮ Generators of quantum Markov semigroups ⋮ E\(_{0}\)-semigroups of type II\(_{0}\) and \(q\)-purity: boundary weight maps of range rank one and two ⋮ \(C^\ast\)-subproduct and product systems ⋮ Arveson's characterisation of CCR flows: the multiparameter case ⋮ The closedness of the generator of a semigroup ⋮ On type II\(_{0}\) \(E_{0}\)-semigroups induced by boundary weight doubles ⋮ The standard form of an \(E_0\)-semigroup ⋮ ON PRODUCT SYSTEMS ARISING FROM SUM SYSTEMS ⋮ A conjugacy criterion for pure \(E_{0}\)-semigroups ⋮ Minimal isometric dilations of operator cocycles ⋮ Quasi-pure \(E_0\)-semigroups ⋮ Generalized CCR flows ⋮ Local unitary cocycles of \(E_0\)-semigroups ⋮ Spatial Markov semigroups admit Hudson-Parthasarathy dilations ⋮ Additive units of product systems ⋮ Cocycles for one-parameter flows of \(\mathfrak B(\mathfrak h)\)

Cites Work

• A non spatial continuous semigroup of *-endomorphisms of \({\mathcal B}({\mathcal H})\)
• An index for continuous semigroups of *-endomorphisms of \({\mathfrak B}({\mathfrak H})\)
• An addition formula for the index of semigroups of endomorphisms of B(H)
• Continuous Spatial Semigroups of ∗-Endomorphisms of ()
• An Index Theory for Semigroups of *-Endomorphisms of and Type II₁ Factors.
• Complete Boolean algebras of type I factors

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