Continuous analogues of Fock space. II. The spectral \(C^*\)-algebra

DOI10.1016/0022-1236(90)90082-VzbMath0715.46039MaRDI QIDQ752422

William Arveson

Publication date: 1990

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

product systemsouter conjugacycontinuous tensor productcontinuous time analogue of the Cuntz algebragauge-invariant closed two-sided idealsreduced \(C^ *\)-algebrasemigroup of normal *-endomorphisms of the algebra B(H)separable \(C^ *\)-algebraspectral \(C^ *\) algebra associated with a product structure

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Noncommutative dynamical systems (46L55) Axiomatic quantum field theory; operator algebras (81T05) General theory of (C^*)-algebras (46L05) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (23)

Positivity and cohomology for involutive semigroups ⋮ QUANTUM MARKOV PROCESSES (CORRESPONDENCES AND DILATIONS) ⋮ Absence of gauge-invariant functionals on spectral \(C^*\)-algebras ⋮ E₀-SEMIGROUPS FOR CONTINUOUS PRODUCT SYSTEMS ⋮ CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond ⋮ Classification of 𝐸₀–semigroups by product systems ⋮ ISOMETRIC DILATIONS OF REPRESENTATIONS OF PRODUCT SYSTEMS VIA COMMUTANTS ⋮ Arveson's characterisation of CCR flows: the multiparameter case ⋮ An Index Theory For Quantum Dynamical Semigroups ⋮ Discrete product systems and their \(C^*\)-algebras ⋮ On \(C^{*}\)-algebra of a semigroup of partial isometries ⋮ A class of essential representations of product systems ⋮ Subsystems of Fock need not be Fock: Spatial CP-semigroups ⋮ Unit vectors, Morita equivalence and endomorphisms ⋮ Quasi-pure \(E_0\)-semigroups ⋮ MEASURABLE -SEMIGROUPS ARE CONTINUOUS ⋮ Continuous analogues of Fock space. IV: Essential states ⋮ A SIMPLE PROOF OF THE FUNDAMENTAL THEOREM ABOUT ARVESON SYSTEMS ⋮ Quantum stochastic calculus on full Fock modules ⋮ EXISTENCE OF E₀-SEMIGROUPS FOR ARVESON SYSTEMS: MAKING TWO PROOFS INTO ONE ⋮ Pure infiniteness of spectral algebras ⋮ COMPLETE CLASSIFICATION OF SPECTRAL OPERATOR ALGEBRAS ASSOCIATED WITH DIVISIBLE PRODUCT SYSTEMS ⋮ The enveloping \(E\)-semigroup of a product system

Cites Work

• A non spatial continuous semigroup of *-endomorphisms of \({\mathcal B}({\mathcal H})\)
• On \(O_ n\).
• Simple \(C^*\)-algebras generated by isometries
• 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 analogues of Fock space
• An Index Theory for Semigroups of *-Endomorphisms of and Type II₁ Factors.
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