Some remarks on the Gelfand–Naimark–Segal representations of topological *-algebras

DOI10.1063/1.2897032zbMath1153.81380arXiv0711.3056OpenAlexW3103826973MaRDI QIDQ3544680

Sergio Manuel Iguri, Mario A. Castagnino

Publication date: 8 December 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.3056

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) General theory of (C^*)-algebras (46L05) Applications of functional analysis in quantum physics (46N50) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) General theory of topological algebras with involution (46K05)

Related Items (3)

Formal features of a general theoretical framework for decoherence in open and closed systems ⋮ On the classical limit of quantum mechanics, fundamental graininess and chaos: compatibility of chaos with the correspondence principle ⋮ Growing classical and quantum entropies in the early universe

Cites Work

• Unbounded GNS representations of a *-algebra in a Krein space
• Unbounded representations of \(^*\)-algebras
• Models of local relativistic quantum fields with indefinite metric (in all dimensions)
• On GNS representations on inner product spaces. I. The structure of the representation space
• The formulation of quantum mechanics in terms of nuclear algebras
• Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of \(Op^*\) algebras and vector states on them
• Self-adjoint algebras of unbounded operators
• Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.)
• On revolutionizing quantum field theory with Tomita’s modular theory
• The quest for understanding in relativistic quantum physics
• Selfadjoint Algebras of Unbounded Operator. II
• Irreducible representations of the Heisenberg algebra in Krein spaces
• On the complexity of the description of *-algebra representations by unbounded operators
• Characterizations of cyclic *-representations with equal weak and strong commutants
• Applications of topological*-algebras of unbounded operators
• Spatial Theory for Algebras of Unbounded Operators. II
• Representations of Hermitian kernels by means of Krein spaces. II. Invariant kernels
• A remark on the deformation of GNS representations of *-algebras

This page was built for publication: Some remarks on the Gelfand–Naimark–Segal representations of topological  *-algebras