References
[AH-K] Albeverio, S., Høegh-Krohn, R.: Dirichlet forms and Markov semigroups onC *-algebras. Commun. Math. Phys.56, 173–187 (1977)
[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)
[ArY] Araki, H., Yamagami, S.: An inequality for Hilbert-Schmidt norm. Commun. Math. Phys.81, 89–96 (1981)
[Con] Connes, A.: Classification of injective factors. Ann. Math.104, 73–115 (1976)
[D1] Davies, E.B.: quantum theory of open systems. London: Academic Press 1976
[D2] Davies, E.B.: One-parameter semigroups. London: Academic Press 1980
[D3] Davies, E.B.: Heat kernels and spectral theory. London New York: Cambridge University Press 1989
[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)
[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)
[Dix] Dixmier, J.: Von Neumann algebras, 2nd ed., transl. F. Jellett Amsterdam: North-Holland 1981
[Ev, D] Evans, D.E.: Quantum dynamical semigroups, symmetry groups, and locality. Acta. Appl. Math.2, 333–352 (1984)
[Ev, M] Evans, M.P.: Existence of quantum diffusions. Probab. Theory Relat. Fields81, 473–483 (1989)
[Gro] Gross, L.: Hypercontractivity and logarithmic Sobolev inequalities for the Clifford-Dirichlet form. Duke. Math. J.42 (no. 3), 383–396 (1975)
[Gui] Guichardet, A.: Symmetric Hilbert spaces and related topics. (Lect. Notes Math., vol. 261) Berlin Heidelberg New York: Springer 1972
[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
[HuP] Hudson, R.L., Parthasarathy, K.R.: Quantum Itô's formula and stochastic evolutions. Commun. Math. Phys.93, 301–323 (1984)
[HuR] Hudson, R.L., Robinson, P.: Quantum diffusions and the non-commutative torus. Lett. Math. Phys.15, 47–53 (1988)
[Kun] Kunze, R.A.:L p Fourier transforms on locally compact unimodular groups. Trans. Am. Math. Soc.89, 519–540 (1958)
[LiY] Li, P., Yau, S.P.: Estimates of eigenvalues of a compact Riemannian manifold. Proc. Symp. Pure Math.36, 205–239 (1980)
[L1] Lindsay, J.M.: Gaussian hypercontractivity revisited. J. Funct. Anal.92, 313–324 (1990)
[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)
[Nel] Nelson, E.: Notes on non-commutative integration. J. Funct. Anal.15, 103–116 (1974)
[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
[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)
[Seg] Segal, I.E.: A non-commutative extension of abstract integration. Ann. Math.57, 401–456 (1953); Correction. Ann. Math.58, 595–596 (1953)
[Sko] Skorohod, A. V.: On a generalisation of a stochastic integral. Theory Probab. Appl.XX, 219–233 (1975)
[Sti] Stinespring, W.F.: Integration theorems for gages and duality for unimodular groups Trans. Am. Math. Soc.,90, 15–56 (1959)
[Yea] Yeadon, F.J.: Non-commutativeL p-spaces. Math. Proc. Camb. Philos. Soc.77, 91–102 (1975)
[Zak] Zakai, M.: The Malliavin calculus., Acta Appl. Math.3, 175–207 (1985)
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Davies, E.B., Lindsay, J.M. Non-commutative symmetric Markov semigroups. Math Z 210, 379–411 (1992). https://doi.org/10.1007/BF02571804
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DOI: https://doi.org/10.1007/BF02571804