Glasnik Matematicki, Vol. 48, No. 2 (2013), 403-414.

QUADRATIC OPERATORS ON AM-SPACES

Włodzimierz Fechner

Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
e-mail: fechner@math.us.edu.pl & wlodzimierz.fechner@us.edu.pl


Abstract.   Our purpose is to deal with quadratic operators acting between vector lattices of continuous mappings on a compact Hausdorff space. In our first main result we characterize quadratic-multiplicative operators, whereas in the second one we provide necessary and sufficient conditions for a quadratic operator to be proportional to the square of a continuous linear operator.

2010 Mathematics Subject Classification.   39B52, 46A40, 46B42, 46E05, 47B60, 47H60.

Key words and phrases.   Quadratic operator, vector lattice, AM-space.


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DOI: 10.3336/gm.48.2.12


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