Infinite dimensional orthogonality preserving nonlinear Markov operators

Farrukh Mukhamedov; Ahmad Fadillah Embong

doi:10.1080/03081087.2019.1607241

Infinite dimensional orthogonality preserving nonlinear Markov operators

Farrukh Mukhamedov, Ahmad Fadillah Embong

Department of Mathematical Sciences

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

6 Citations (Scopus)

Abstract

In the present paper, we study infinite dimensional orthogonality preserving the second-order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear Markov operators is equivalent to the orthogonality preserves in the class of π-Volterra operators. Moreover, a full description of such kind of operators has been found in terms of heredity coefficients. Besides, we are able to represent these operators their canonical forms. Furthermore, some properties of orthogonality preserving the second-order nonlinear operators and their fixed points are studied.

Original language	English
Pages (from-to)	526-550
Number of pages	25
Journal	Linear and Multilinear Algebra
Volume	69
Issue number	3
DOIs	https://doi.org/10.1080/03081087.2019.1607241
Publication status	Published - 2021

Keywords

Nonlinear Markov operator
fixed points
infinite dimensional
orthogonality preserving
surjective

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081087.2019.1607241

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abstract = "In the present paper, we study infinite dimensional orthogonality preserving the second-order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear Markov operators is equivalent to the orthogonality preserves in the class of π-Volterra operators. Moreover, a full description of such kind of operators has been found in terms of heredity coefficients. Besides, we are able to represent these operators their canonical forms. Furthermore, some properties of orthogonality preserving the second-order nonlinear operators and their fixed points are studied.",

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AU - Mukhamedov, Farrukh

AU - Fadillah Embong, Ahmad

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Y1 - 2021

N2 - In the present paper, we study infinite dimensional orthogonality preserving the second-order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear Markov operators is equivalent to the orthogonality preserves in the class of π-Volterra operators. Moreover, a full description of such kind of operators has been found in terms of heredity coefficients. Besides, we are able to represent these operators their canonical forms. Furthermore, some properties of orthogonality preserving the second-order nonlinear operators and their fixed points are studied.

AB - In the present paper, we study infinite dimensional orthogonality preserving the second-order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear Markov operators is equivalent to the orthogonality preserves in the class of π-Volterra operators. Moreover, a full description of such kind of operators has been found in terms of heredity coefficients. Besides, we are able to represent these operators their canonical forms. Furthermore, some properties of orthogonality preserving the second-order nonlinear operators and their fixed points are studied.

KW - Nonlinear Markov operator

KW - fixed points

KW - infinite dimensional

KW - orthogonality preserving

KW - surjective

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

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ER -

Infinite dimensional orthogonality preserving nonlinear Markov operators

Abstract

Keywords

ASJC Scopus subject areas

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