Abstract
Quantum Mechanics associates to observables self-adjoint operators on a Hilbert space, to pure states orthogonal projections on one-dimensional subspaces and describes the evolution as a one-parameter group of unitary operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Araki, H. (1964). Progress of Theoretical Physics, 32, 956–965.
Arveson, A. (1976). Invitation to \(C^*\) -algebras. New York: Springer.
Bratteli, O. (1986). Derivations, dissipations and group action on \(C^*\) -algebras LNM. New York: Springer.
Christensen, A. (1979). Journal of the London Mathematical Society, 20, 358–376.
Dell’Antonio, G. F. (1967). Communications on Pure and Applied Mathematics, 20, 413–429.
Diximier, J. (1981). von Neumann Algebras. Amsterdam: North-Holland.
Dixmier \(C^*\)-algebres Gallimard Paris.
Gel’fand, I., & Neimark, M. (1943). Matematicheskii Sbornik, 12, 197–217.
Kadison, J. R. (1951). Annals of Mathematics, 54, 325–338.
Kadison, R. (1963). Annals of Mathematics, 83, 273–298.
Kadison, R., & Ringrose, J. Introduction to \(C^*\) -algebras (vol I, II)
Pedersen, G. K. (Ed.). (1979). \(C^* \)-algebras and their automorphism groups. St Louis: Academic Press.
Ringrose, J. (1972). London Mathematical Society, 5, 432–450.
Sakai, H. (1960). Tohoku Mathematical Journal, 12, 31–59.
Saunders, V. S. (1986). Invitationto von neumann algebras. New York: Springer.
Segal, I. (1947). Bulletin of the American Mathematical Society, 53, 73–88.
Störmer, E. (1965). Transactions of the AMS, 120, 438–447.
Takesaki, M. (2002, 2003). Theory of operator Algebras I, II, III Encyclopaedia of Mathematical Sciences (Vols. 124, 125, 127). Berlin: Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Atlantis Press and the author(s)
About this chapter
Cite this chapter
Dell’Antonio, G. (2015). Lecture 9: Elements of \(C^*\)-algebras, GNS Representation, Automorphisms and Dynamical Systems. In: Lectures on the Mathematics of Quantum Mechanics I. Atlantis Studies in Mathematical Physics: Theory and Applications, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-118-5_9
Download citation
DOI: https://doi.org/10.2991/978-94-6239-118-5_9
Published:
Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-6239-117-8
Online ISBN: 978-94-6239-118-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)