$L^p$-spaces and quantum dynamical semigroups

• Autorzy: Stanisław Goldstein , J. Martin Lindsay
• Języki publikacji: EN

Słowa kluczowe

EN

C*-algebra; symmetric embedding; von Neumann algebra; weight; $L^p$-space; Markov semigroup; positivity; KMS-symmetry; Dirichlet form

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 43
• Numer: 1
• Strony: 211-216

Daty

wydano

1998

Twórcy

autor

Stanisław Goldstein

• Faculty of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

autor

J. Martin Lindsay

• Department of Mathematics, University of Nottingham, Nottingham NG7 2RD, U.K.

Bibliografia

• [AH-K] S. Albeverio and R. Høegh-Krohn, Dirichlet forms and Markov semigroups on C*-algebras, Comm. Math. Phys. 56 (1977), 173-187.
• [Cip] F. Cipriani, Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras, J. Funct. Anal. 147 (1977), 259-300.
• [CFL] F. Cipriani, F. Fagnola and J. M. Lindsay, Spectral analysis and Feller property for the quantum Ornstein-Uhlenbeck semigroup, preprint, 1997.
• [Dav] E. B. Davies, Analysis on graphs and noncommutative geometry, J. Funct. Anal. 111 (1993), 398-430.
• [DL 1] E. B. Davies and J. M. Lindsay, Noncommutative symmetric Markov semigroups, Math. Z. 210 (1992), 379-411.
• [DL 2] E. B. Davies and J. M. Lindsay, Superderivations and symmetric Markov semigroups, Comm. Math. Phys. 157 (1993), 359-370.
• [GL 1] S. Goldstein and J. M. Lindsay, KMS-symmetric Markov semigroups, Math. Z. 219 (1995), 591-608.
• [GL 2] S. Goldstein and J. M. Lindsay, Markov semigroups KMS-symmetric for a weight, preprint, 1997.
• [GL 3] S. Goldstein and J. M. Lindsay, Noncommutative interpolation and Markov semigroups, in preparation.
• [GPh] S. Goldstein and V. T. Phan, $L^p$-spaces for UHF algebras, to appear in Internat. J. Theoret. Phys., 1998.
• [GIS] R. Guido, T. Isola and S. Scarlatti, Non-symmetric Dirichlet forms on semifinite von Neumann algebras, J. Funct. Anal. 135 (1996), 50-75.
• [Haa] U. Haagerup, $L^p$-spaces associated with an arbitrary von Neumann algebra, in: Algèbres d'Opérateurs et leur Application en Physique Mathématique. Colloques Internationaux du CNRS, no. 274, Marseille, 20-24 juin 1977, Éditions du CNRS, Paris, 1979, 175-184.
• [MZ 1] A. W. Majewski and B. Zegarliński, Quantum stochastic dynamics I: Spin Systems on a lattice, Math. Phys. Electron. J. 1 (1995), no. 1.
• [MZ 2] A. W. Majewski and B. Zegarliński, On quantum stochastic dynamics. Disordered systems and statistical physics: rigorous results (Budapest, 1995), Markov Process. Related Fields 2 (1996), 87-116.
• [Mat] T. Matsui, Markov semigroups on UHF algebras, Rev. Math. Phys. 5 (1993), 587-600.
• [Sau] J.-L. Sauvageot, Semigroupe de la chaleur transverse sur la C*-algèbre d'un feuilletage riemannien, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 531-536.
• [Te 1] M. Terp, $L^p$-spaces associated with von Neumann algebras, notes, Report No. 3a + 3b, Københavns Universitets Matematiske Institut, 1981.
• [Te 2] M. Terp, Interpolation spaces between a von Neumann algebra and its predual, J. Operator Theory 8 (1982), 327-360.