Partial \({}^*\)-algebras of closable operators. I: The basic theory and the abelian case

DOI10.2977/prims/1195171084zbMath0724.47020OpenAlexW2046364905MaRDI QIDQ757807

Camillo Trapani, Atsushi Inoue, Jean-Pierre Antoine

Publication date: 1990

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195171084

zbMATH Keywords

abelian partial *-algebras bounded commutant partial *-algebras of closable operators in a Hilbert space partial \(Op^ *\)-algebras partial \(Op^ *\)-algebras generated by a single symmetric operator and their bounded commutants quasi-weak representations of abstract partial *-algebras

Mathematics Subject Classification ID

Algebras of unbounded operators; partial algebras of operators (47L60) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) General theory of topological algebras with involution (46K05)

Related Items (30)

TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES ⋮ On the regularity of the partial \(O^*\)-algebras generated by a closed symmetric operator ⋮ Complete sets of non-self-adjoint observables: An unbounded approach ⋮ General properties between the canonical correlation and the independent-oscillator model on a partial *-algebra ⋮ The Heisenberg dynamics of spin systems: A quasi*-algebras approach ⋮ Extension of unbounded left Hilbert algebras to partial *-algebras ⋮ Partial *-algebras and Volterra convolution of distribution kernels ⋮ Unnamed Item ⋮ Normal forms on partial O*-algebras ⋮ Completely positive conjugate-bilinear maps on partial *-algebras ⋮ Modular structure of algebras of unbounded operators ⋮ Modular systems induced by trace functionals on algebras of unbounded operators ⋮ Quasi *-algebras and multiplication of distributions ⋮ Strongly Cyclic Vectors for PartialOp*-Algebras ⋮ \(CQ^*\)-algebras: Structure properties ⋮ Representation of completely positive maps between partial *-algebras ⋮ Spatial theory of *-automorphisms of partial O*-algebras ⋮ Extension of representations in quasi *-algebras ⋮ Spatiality of *-derivations of partial O*-algebras ⋮ Structure of locally convex quasi \(C^*\)-algebras ⋮ Biweights on partial *-algebras ⋮ Standard partial \(O^*\)-algebras ⋮ Partial \(\star\)-algebras of closable operators. II: States and representations of partial \(\star\)-algebras ⋮ Unbounded \(C^{\ast}\)-seminorms, biweights, and \(^{\ast}\)-representations of partial \(^{\ast}\)-algebras: A review ⋮ Unbounded \(C^*\)-seminorms and \(*\)-representations of partial \(*\)-algebras ⋮ Representability of invariant positive sesquilinear forms on partial *-algebras ⋮ Unnamed Item ⋮ Radon--Nikodým theorem for biweights and regular biweights on partial *-algebras ⋮ Noncommutative mean ergodic theorem for partial \(W^*\)-dynamical semigroups ⋮ Unnamed Item

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