Infinite dimensional orthogonality preserving nonlinear Markov operators

Farrukh Mukhamedov, Ahmad Fadillah Embong

Research output: Contribution to journalArticlepeer-review

4 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 languageEnglish
Pages (from-to)526-550
Number of pages25
JournalLinear and Multilinear Algebra
Volume69
Issue number3
DOIs
Publication statusPublished - 2021

Keywords

  • Nonlinear Markov operator
  • fixed points
  • infinite dimensional
  • orthogonality preserving
  • surjective

ASJC Scopus subject areas

  • Algebra and Number Theory

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