publication . Preprint . Conference object . 2003

Independence and Product Systems

Michael Skeide;
Open Access English
  • Published: 26 Aug 2003
Abstract
Starting from elementary considerations about independence and Markov processes in classical probability we arrive at the new concept of conditional monotone independence (or operator-valued monotone independence). With the help of product systems of Hilbert modules we show that monotone conditional independence arises naturally in dilation theory.
Subjects
free text keywords: Mathematics - Operator Algebras, Mathematics - Probability, 60J25, 46L55, 46L53, 60A05, Mathematics, Manufacturing engineering, Product system
23 references, page 1 of 2

[Arv89] W. Arveson. Continuous analogues of Fock space. Number 409 in Mem. Amer. Math. Soc. American Mathematical Society, 1989.

[BGS99] A. Ben Ghorbal and M. Schu¨rmann. On the algebraic foundations of non-commutative probability theory. Preprint, Nancy, 1999.

[Bha96] B.V.R. Bhat. An index theory for quantum dynamical semigroups. Trans. Amer. Math. Soc., 348:561-583, 1996.

[BS00] B.V.R. Bhat and M. Skeide. Tensor product systems of Hilbert modules and dilations of completely positive semigroups. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 3:519-575, 2000.

[LM95] H. van Leeuwen and H. Maassen. An obstruction for q-deformation on the convolution product. Preprint, Nijmegen, 1995.

[Lu97] Y.G. Lu. An interacting free Fock space and the arcsine law. Prob. Math. Statist., 17:149- 166, 1997.

[MSS03] P.S. Muhly, M. Skeide, and B. Solel. (Tentative title) On product systems of W ∗-modules and their commutants. Preprint, Campobasso, in preparation, 2003. [OpenAIRE]

[Mur97] N. Muraki. Noncommutative Brwonian in monotone Fock space. Commun. Math. Phys., 183:557-570, 1997. [OpenAIRE]

[Mur02] N. Muraki. The five independences as quasi-universal products. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5:113-134, 2002.

[Pas73] W.L. Paschke. Inner product modules over B∗-algebras. Trans. Amer. Math. Soc., 182:443-468, 1973.

[PS72] K.R. Parthasarathy and K. Schmidt. Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. Number 272 in Lect. Notes Math. Springer, 1972.

[Rie74] M.A. Rieffel. Induced representations of C∗-algebras. Adv. Math., 13:176-257, 1974. [OpenAIRE]

[Sch95] M. Schu¨rmann. Non-commutative probability on algebraic structures. In H. Heyer, editor, Probability measures on groups and related structures XI, pages 332-356. World Sci. Publishing, 1995.

[Ske99] M. Skeide. A central limit theorem for Bose Z-independent quantum random variables. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2:289-299, 1999.

[Ske00] M. Skeide. Quantum stochastic calculus on full Fock modules. J. Funct. Anal., 173:401- 452, 2000. [OpenAIRE]

23 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Conference object . 2003

Independence and Product Systems

Michael Skeide;