Skip to main content
Log in

Non-commutative symmetric Markov semigroups

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [AH-K] Albeverio, S., Høegh-Krohn, R.: Dirichlet forms and Markov semigroups onC *-algebras. Commun. Math. Phys.56, 173–187 (1977)

    Article  MATH  Google Scholar 

  • [AIR] Albeverio, S., Röckner, M.: Classical Dirichlet Forms on Topological Vector Spaces—Closability and a Cameron-Martin formula. J. Funct. anal.88 (no. 2), 395–436 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • [ArY] Araki, H., Yamagami, S.: An inequality for Hilbert-Schmidt norm. Commun. Math. Phys.81, 89–96 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • [Con] Connes, A.: Classification of injective factors. Ann. Math.104, 73–115 (1976)

    Article  MathSciNet  Google Scholar 

  • [D1] Davies, E.B.: quantum theory of open systems. London: Academic Press 1976

    MATH  Google Scholar 

  • [D2] Davies, E.B.: One-parameter semigroups. London: Academic Press 1980

    MATH  Google Scholar 

  • [D3] Davies, E.B.: Heat kernels and spectral theory. London New York: Cambridge University Press 1989

    MATH  Google Scholar 

  • [DL] Davies, E.B., Lindsay, J.M.: Superderivations and symmetric Markov semigroups. (Preprint 1991)

  • [DR1] Davies, E.B., Rothaus, O.S.: Markov semigroups onC *-bundles J. Funct. Anal.85 (no. 2), 264–286 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  • [DR2] Davies, E.B., Rothaus, O.S.: A BLW inequality for vector bundles and applications to spectral bounds. J. Funct. Anal.86, (no. 2), 390–410 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  • [Dix] Dixmier, J.: Von Neumann algebras, 2nd ed., transl. F. Jellett Amsterdam: North-Holland 1981

    Google Scholar 

  • [Ev, D] Evans, D.E.: Quantum dynamical semigroups, symmetry groups, and locality. Acta. Appl. Math.2, 333–352 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  • [Ev, M] Evans, M.P.: Existence of quantum diffusions. Probab. Theory Relat. Fields81, 473–483 (1989)

    MATH  Google Scholar 

  • [Gro] Gross, L.: Hypercontractivity and logarithmic Sobolev inequalities for the Clifford-Dirichlet form. Duke. Math. J.42 (no. 3), 383–396 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  • [Gui] Guichardet, A.: Symmetric Hilbert spaces and related topics. (Lect. Notes Math., vol. 261) Berlin Heidelberg New York: Springer 1972

    MATH  Google Scholar 

  • [Hud] Hudson, R.L.: Algebraic theory of quantum diffusions, In: Truman, A., Davies, I.M. (es.) Stochastic Mechanics and Stochastic Processes. Proceedings, Swansea 1986. (Lect. Notes Math., vol. 1325, pp. 113–124) Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  • [HuP] Hudson, R.L., Parthasarathy, K.R.: Quantum Itô's formula and stochastic evolutions. Commun. Math. Phys.93, 301–323 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  • [HuR] Hudson, R.L., Robinson, P.: Quantum diffusions and the non-commutative torus. Lett. Math. Phys.15, 47–53 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • [Kun] Kunze, R.A.:L p Fourier transforms on locally compact unimodular groups. Trans. Am. Math. Soc.89, 519–540 (1958)

    Article  MathSciNet  Google Scholar 

  • [LiY] Li, P., Yau, S.P.: Estimates of eigenvalues of a compact Riemannian manifold. Proc. Symp. Pure Math.36, 205–239 (1980)

    MathSciNet  Google Scholar 

  • [L1] Lindsay, J.M.: Gaussian hypercontractivity revisited. J. Funct. Anal.92, 313–324 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • [L2] Lindsay, J.M.: On generalised quantum stochastic integrals. (Preprint 1990)

  • [MuN] Murray, F.J., von Neumann, J.: On rings of operators II. Trans. Am. Math. Soc.41, 208–248 (1937)

    Article  MATH  Google Scholar 

  • [Nel] Nelson, E.: Notes on non-commutative integration. J. Funct. Anal.15, 103–116 (1974)

    Article  MATH  Google Scholar 

  • [Sa1] Sauvageot, J.-L.: Quantum Dirichlet forms, differential calculus and semigroups. In: Quantum probability and applications V. Proceedings, Heidelberg 1988. Accardi, L., von Waldenfels, W. (eds.), (Lect. Notes Math., vol. 1442, pp. 334–346) Berlin Heidelberg New York: Springer 1990

    Chapter  Google Scholar 

  • [Sa2] Sauvageot, J.-L.: Semi-groupe de la chaleur transverse sur laC *-algèbre d'un feulletage riemannien. C.R. Acad. Sci. Paris, Sér. I310, 531–536 (1990)

    MATH  MathSciNet  Google Scholar 

  • [Seg] Segal, I.E.: A non-commutative extension of abstract integration. Ann. Math.57, 401–456 (1953); Correction. Ann. Math.58, 595–596 (1953)

    Article  Google Scholar 

  • [Sko] Skorohod, A. V.: On a generalisation of a stochastic integral. Theory Probab. Appl.XX, 219–233 (1975)

    Google Scholar 

  • [Sti] Stinespring, W.F.: Integration theorems for gages and duality for unimodular groups Trans. Am. Math. Soc.,90, 15–56 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  • [Yea] Yeadon, F.J.: Non-commutativeL p-spaces. Math. Proc. Camb. Philos. Soc.77, 91–102 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  • [Zak] Zakai, M.: The Malliavin calculus., Acta Appl. Math.3, 175–207 (1985)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Marshall Stone

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davies, E.B., Lindsay, J.M. Non-commutative symmetric Markov semigroups. Math Z 210, 379–411 (1992). https://doi.org/10.1007/BF02571804

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571804

Keywords

Navigation