FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 3, PAGES 3-11

Invertibility of linear f-order preservers

A. A. Alieva

Abstract

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In this paper, we prove that monotonic linear transformations with respect to partial orders $ \stackrel {*}{<}_f $, $ {*}{<}_f $, $ {<}{*}_f $, $ \stackrel {\diamond}{<}_f $, $ \stackrel {\sigma}{<}_f $ and $ \stackrel {\sigma_1}{<}_f $ are invertible.

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