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Invertibility of linear f-order preservers

Abstract

In this paper, we prove that monotonic linear transformations with respect to partial orders \(\mathop { < _f }\limits^ * , * < _f , < * _f ,\mathop { < _f }\limits^\diamondsuit ,\mathop { < _f }\limits^\sigma \) and \(\mathop { < _f }\limits^{\sigma 1} \) are invertible.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 3–11, 2003.

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Alieva, A.A. Invertibility of linear f-order preservers. J Math Sci 135, 3269–3275 (2006). https://doi.org/10.1007/s10958-006-0156-0

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Keywords

  • Partial Order
  • Linear Transformation