On quantum quadratic operators of M2(C) and their dynamics

F. Mukhamedov Farrukh; Hasan Akin; Seyit Temir; Abduaziz Abduganiev

doi:10.1016/j.jmaa.2010.10.047

On quantum quadratic operators of M2(C) and their dynamics

F. Mukhamedov Farrukh
, Hasan Akin
, Seyit Temir
, Abduaziz Abduganiev

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of 2×2 matrices M2(C). First, we describe q.q.o. with Haar state as well as quadratic operators with the Kadison-Schwarz property. By means of such a description we provide an example of q.q.o. which is not the Kadison-Schwarz operator. Then we study stability of dynamics of q.q.o.

Original language	English
Pages (from-to)	641-655
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	376
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2010.10.047
Publication status	Published - Apr 15 2011
Externally published	Yes

Keywords

Kadison-Schwarz operator
Nonlinear dynamics
Quadratic operator
Quantum quadratic operators
Stability

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2010.10.047

Cite this

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title = "On quantum quadratic operators of M2(C) and their dynamics",

abstract = "In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of 2×2 matrices M2(C). First, we describe q.q.o. with Haar state as well as quadratic operators with the Kadison-Schwarz property. By means of such a description we provide an example of q.q.o. which is not the Kadison-Schwarz operator. Then we study stability of dynamics of q.q.o.",

keywords = "Kadison-Schwarz operator, Nonlinear dynamics, Quadratic operator, Quantum quadratic operators, Stability",

author = "\{Mukhamedov Farrukh\}, F. and Hasan Akin and Seyit Temir and Abduaziz Abduganiev",

note = "Funding Information: The first named author (F.M.) thanks the Scientific and Technological Research Council of Turkey (TUBITAK) for support and Harran University for kind hospitality. Moreover, he and the forth named author (A.A.) also acknowledge Research Endowment Grant B (EDW B 0905-303) of IIUM and the MOSTI grant 01-01-08-SF0079. Finally, authors would like to thank to an anonymous referee whose useful suggestions and comments improve the content of the paper.",

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doi = "10.1016/j.jmaa.2010.10.047",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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AU - Mukhamedov Farrukh, F.

AU - Akin, Hasan

AU - Temir, Seyit

AU - Abduganiev, Abduaziz

N1 - Funding Information: The first named author (F.M.) thanks the Scientific and Technological Research Council of Turkey (TUBITAK) for support and Harran University for kind hospitality. Moreover, he and the forth named author (A.A.) also acknowledge Research Endowment Grant B (EDW B 0905-303) of IIUM and the MOSTI grant 01-01-08-SF0079. Finally, authors would like to thank to an anonymous referee whose useful suggestions and comments improve the content of the paper.

PY - 2011/4/15

Y1 - 2011/4/15

N2 - In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of 2×2 matrices M2(C). First, we describe q.q.o. with Haar state as well as quadratic operators with the Kadison-Schwarz property. By means of such a description we provide an example of q.q.o. which is not the Kadison-Schwarz operator. Then we study stability of dynamics of q.q.o.

AB - In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of 2×2 matrices M2(C). First, we describe q.q.o. with Haar state as well as quadratic operators with the Kadison-Schwarz property. By means of such a description we provide an example of q.q.o. which is not the Kadison-Schwarz operator. Then we study stability of dynamics of q.q.o.

KW - Kadison-Schwarz operator

KW - Nonlinear dynamics

KW - Quadratic operator

KW - Quantum quadratic operators

KW - Stability

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UR - https://www.scopus.com/pages/publications/78650700018#tab=citedBy

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DO - 10.1016/j.jmaa.2010.10.047

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VL - 376

SP - 641

EP - 655

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On quantum quadratic operators of M2(C) and their dynamics

Abstract

Keywords

ASJC Scopus subject areas

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