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Geometry on the quantum Heisenberg manifold
  • Partha Sarathi Chakraborty, K. Sinha
  • Mathematics
  • 24 December 2001
Abstract A class of C ∗ -algebras called quantum Heisenberg manifolds were introduced by Rieffel in (Comm. Math. Phys. 122 (1989) 531) as strict deformation quantization of Heisenberg manifolds.Expand
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Stochastic Integral Representation of Bounded Quantum Martingales in Fock Space
It is a classical theorem of Kunita and Watanabe [6] that every square integrable martingale adapted to the standard Brownian motion can be uniquely expressed as the stochastic integral of aExpand
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Quantum random walk revisited
In the framework of the symmetric Fock space over L 2 (R + ), the details of the approximation of the four fundamental quantum stochastic increments by the four appropriate spin-matrices are studied.Expand
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On pairs of projections in a Hilbert space
We give an algebraic derivation of the canonical form of a generic pair of projections. The result is used to determine the spectral shift of a pair of projections and various properties of FredholmExpand
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Spectral shift function and trace formula
The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii)Expand
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Hilbert Modules and Stochastic Dilation of a Quantum Dynamical Semigroup on a von Neumann Algebra
Abstract:A general theory for constructing a weak Markov dilation of a uniformly continuous quantum dynamical semigroup Tt on a von Neumann algebra ? with respect to the Fock filtration is developedExpand
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Quantum Stochastic Processes and Noncommutative Geometry
1. Introduction 2. Preliminaries 3. Quantum dynamical semigroups 4. Hilbert modules 5. Quantum stochastic calculus with bounded coefficients 6. Dilation of quantum dynamical semigroups with boundedExpand
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Quantum stop times
The notion of stop-time can be naturally translated in a quantum probabilistic framework and this problem has been studied by several authors [1], [2], [3], [4], [5]. Recently Parthasarathy and SinhaExpand
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