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Characteristic Functions for Ergodic Tuples
Santanu Dey,Rolf Gohm +1 more
TL;DR: It is proved that the characteristic function is a complete unitary invariant for such tuples and show how it can be computed.
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Abstract: Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G. Popescu. We prove that our characteristic function is a complete unitary invariant for such tuples and show how it can be computed.
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Citations
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Non-Commutative Markov Chains and Multi-Analytic Operators
TL;DR: In this article, a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain is studied, and it is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory.
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Characteristic Functions of Liftings
Santanu Dey,Rolf Gohm +1 more
TL;DR: In this article, the authors introduce characteristic functions for certain contractive liftings of row contractions, which are multi-analytic operators which classify the liftings up to unitary equivalence and provide a kind of functional model.
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Generalized repeated interaction model and transfer functions
Santanu Dey,Kalpesh J. Haria +1 more
TL;DR: In this paper, the authors introduce a toy model of repeated interactions between quantum systems, where an outgoing Cuntz scattering system involving two wandering subspaces is associated to an input/output linear system which leads to a transfer function.
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Weak Markov processes as linear systems
TL;DR: A noncommutative Fornasini–Marchesini system can be realized within a weak Markov process and new insights are gained into stationary Markov chains where observability for the system is closely related to asymptotic completeness in a scattering theory for the chain.
Functional Models and Minimal Contractive Liftings
TL;DR: In this paper, a one-to-one correspondence between unitary equivalence classes of minimal contractive liftings of a row contraction and injective symbols of contractive multi-analytic operators is established.
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