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On Kadison-Schwarz type quantum quadratic operators on \(\mathbb M_2(\mathbb C)\). (English) Zbl 1276.81056

The authors study the description of Kadison-Schwarz type quantum quadratic operators (q.q.o.) acting from \(\mathbb M_2(\mathbb C)\) into \(\mathbb M_2(\mathbb C) \oplus \mathbb M_2 (\mathbb C)\). An example of q.q.o. is provided which is not a Kadison-Schwarz operator and its dynamics is studied. It is stressed that q.q.o. is a generalization of quantum convolution.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
44A35 Convolution as an integral transform
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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