Abstract
We review the main points in the development of partial *-algebras during the last 15 years, at three different levels. (i) The algebraic structure stemming from the partial multiplication; (ii) The topological partial *-algebras; (iii) The partial *-algebras of closable operators in Hilbert spaces or partial O*-algebras, including the representation theory of the abstract partial *-algebras.
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
Preview
Unable to display preview. Download preview PDF.
References
Antoine, J-P., Grossmann, A., (1976): Partial inner product spaces. I. General properties. II. Operators, J. Funct. Anal. 23, 369–378, 379–391
Antoine, J-P., (1980): Partial inner product spaces. III. Compatibility relations revisited. IV. Topological considerations, J. Math. Phys. 21, 268–279, 2067–2079
Antoine, J-P., Gustafson, K., (1981): Partial inner product spaces and semi-inner product spaces, Adv. in Math. 41, 281–300
Antoine, J-P., Karwowski, W., (1983): Partial *-algebras of closed operators, in Quantum Theory of Particles and Fields, pp. 13–30; B. Jancewicz and J. Lukierski (eds.), World Scientific, Singapore
Antoine, J-P., Karwowski, W., (1985): Partial *-algebras of closed linear operators in Hilbert space, Publ. RIMS, Kyoto Univ. 21, 205–236; Add./Err. ibid. 22, (1986) 507–511
Antoine, J-P., Mathot, F., (1987): Partial *-algebras of closed operators and their commutants. I. General structure, Ann. Inst. H. Poincaré 46, 299–324
Antoine, J-P., Inoue, A., Trapani, C., (1994): Spatial theory of *-automorphisms on partial O*-algebras, J. Math. Phys. 35, 3059–3073
Antoine, J-P., Soulet, Y., Trapani, C., (1995): Weights on partial *-algebras, J. Math. Anal. Appl. 192, 920–941
Antoine, J-P., Inoue, A., Trapani, C., (1996): Partial *-algebras of closable operators: A review, Reviews Math. Phys. 8, 1–42
Antoine, J-P., Inoue, A., Ogi, H., (1997): Standard generalized vectors for partial O*-algebras, Ann. Inst. H. Poincaré 67, 223–258
Antoine, J-P., Inoue, A., Trapani, C., (1998): Biweights on partial *-algebras, preprint UCL-98-11, Louvain-la-Neuve (submitted)
Antoine, J-P., Bagarello, F., Trapani, C., (1998): Topological partial *-algebras: Basic properties and examples, Reviews Math. Phys. 10, (to appear)
dell’Antonio, G.F., (1966): On some groups of automorphisms of physical observables, Commun. Math. Phys. 2, 384–397
Bergh, J., Löfström, J., (1976): Interpolation Spaces, Springer, Berlin
Borchers, H.J., (1966): Energy and momentum as observables in quantum field theory, Commun. Math. Phys. 2, 49–54
Bratteli, O., Robinson, D.W., (1979): Operator Algebras and Quantum Statistical Mechanics I, II, Springer-Verlag, Berlin
Dixmier, J., (1957), (1969): Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Gauthier-Villars, Paris
Fournier, J.J.F., Stewart, J., (1985): Amalgams of L p and l q, Bull. Amer. Math. Soc. 13, 1–21
Kadison, R.V., Ringrose, J.R., (1967): Derivations and automorphisms of operator algebras, Commun. Math. Phys. 4, 32–63
Schmüdgen, K., (1990): Unbounded Operator Algebras and Representation Theory, Akademie-Verlag, Berlin
Stratila, S., Zsidó, L., (1979): Lectures on von Neumann Algebras, Abacus Press, Tunbridge Wells (England)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Antoine, JP. (2000). Partial *-Algebras: A Retrospective. In: Borowiec, A., Cegła, W., Jancewicz, B., Karwowski, W. (eds) Theoretical Physics Fin de Siècle. Lecture Notes in Physics, vol 539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46700-9_11
Download citation
DOI: https://doi.org/10.1007/3-540-46700-9_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66801-5
Online ISBN: 978-3-540-46700-7
eBook Packages: Springer Book Archive