Hostname: page-component-7dd5485656-frp75 Total loading time: 0 Render date: 2025-10-31T21:29:41.866Z Has data issue: false hasContentIssue false
  • English
  • Français

Hilbert Bimodules with Involution

Published online by Cambridge University Press:  20 November 2018

Nik Weaver
Nik Weaver*
Affiliation:
Department of Mathematics Washington University St. Louis, Missouri 63130 U.S.A., e-mail: nweaver@math.wustl.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We examine Hilbert bimodules which possess a (generally unbounded) involution. Topics considered include a linking algebra representation, duality, locality, and the role of these bimodules in noncommutative differential geometry

Keywords

46L0846L5746L87

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 3 , 01 September 2001 , pp. 355 - 369
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] Akemann, C. A., personal communication.Google Scholar
[2] Akemann, C. A., J. Anderson and Pedersen, G. K., Excising states of C*-algebras. Canad. J. Math. 38 (1986), 1239–1260.Google Scholar
[3] Arveson, W., Dynamical invariants for noncommutative flows. Operator algebras and quantum field theory (Rome, 1996), Internat. Press, 1998, 476–514.Google Scholar
[4] Bratteli, O. and Robinson, D. W., Operator Algebras and Quantum Statistical Mechanics I. (second edition), Springer-Verlag, 1987.Google Scholar
[5] Connes, A., C* algèbres et géométrie différentielle. C. R. Acad. Sci. Paris Sér. A 290(1980), A599–A604.Google Scholar
[6] Evans, D. E. and Lewis, J. T., Dilations of irreversible evolutions in algebraic quantum theory. Comm. Dublin Inst. Adv. Stud. Ser. A 24(1977).Google Scholar
[7] Falcone, T. and Takesaki, M., Operator valued weights without structure theory. Trans. Amer.Math. Soc. 351 (1999), 323–341.Google Scholar
[8] Fell, J. M. G., An extension of Mackey's method to Banach *-algebraic bundles. Mem. Amer.Math. Soc. 90(1969).Google Scholar
[9] Hartshorne, R., Algebraic Geometry. Springer-Verlag, Graduate Texts in Math. 52, 1977.Google Scholar
[10] Kadison, R. V. and Ringrose, J. R., Fundamentals of the Theory of Operator Algebras II. Academic Press, 1986.Google Scholar
[11] Lance, C., Hilbert C*-modules, LMS Lecture Note Series 210, Cambridge University Press, 1995.Google Scholar
[12] Paschke, W. L., Inner product modules over B*-algebras. Trans. Amer.Math. Soc. 182 (1973), 443–468.Google Scholar
[13] Pedersen, G. K., C*-algebras and their Automorphism Groups. Academic Press, 1979.Google Scholar
[14] Phillips, N. C. and Weaver, N., Modules with norms which take values in a C*-algebra. Pacific J. Math. 185 (1998), 163–181.Google Scholar
[15] Rieffel, M. A., Induced representations of C*-algebras. Adv. Math. 13 (1974), 176–257.Google Scholar
[16] Rieffel, M. A., Morita equivalence for C*-algebras andW*-algebras. J. Pure Appl. Algebra 5 (1974), 51–96.Google Scholar
[17] Rieffel, M. A., Morita equivalence for operator algebras. Proc. Symp. Pure Math. 38 (1982), 285–298.Google Scholar
[18] Sauvageot, J.-L., Tangent bimodule and locality for dissipative operators on C*-algebras. Quantum Probability and App. IV, Springer, Lecture Notes in Math. 1396, 1989, 322–338.Google Scholar
[19] Sauvageot, J.-L., Quantum Dirichlet forms, differential calculus and semigroups. Quantum Probability and App. V, Springer, Lecture Notes in Math. 1442, 1990, 334–346.Google Scholar
[20] Skeide, M., Hilbert modules in quantum electro dynamics and quantum probability. Comm. Math. Phys. 192 (1998), 569–604.Google Scholar
[21] Swan, R. G., Vector bundles and projective modules. Trans. Amer. Math. Soc. 105 (1962), 264–277.Google Scholar
[22] Takehashi, A., Fields of Hilbert Modules. Dissertation, Tulane University, 1971.Google Scholar
[23] Weaver, N., Lipschitz algebras and derivations of von Neumann algebras. J. Funct. Anal. 139 (1996), 261–300.Google Scholar
[24] Woronowicz, S. L., Differential calculus on compact matrix pseudogroups (quantum groups). Comm. Math. Phys. 122 (1989), 125–170.Google Scholar