Infinite dimensional orthogonality preserving nonlinear Markov operators

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.

Keywords:

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

Mathematics Subject Classifications:

• 46L35
• 46L55
• 46A37

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The present work is supported by the United Arab Emirates University – UAEU ‘Start-Up’ Grant, no. 31S259.