Two-sided sgut-majorization and its linear preservers

Document Type : Research Paper

Author

Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box: 7713936417, Rafsanjan, Iran

Abstract

Let $\textbf{M}_{n,m}$ be the set of all $n$-by-$m$ real matrices, and let $\mathbb{R}^{n}$ be  the set of all $n$-by-$1$ real vectors. An $n$-by-$m$ matrix $R=[r_{ij}]$ is called g-row substochastic if $\sum_{k=1}^{m} r_{ik}\leq 1$  for all $i\
    (1\leq i \leq n)$.  For $x$, $y \in \mathbb{R}^{n}$, it is said that $x$ is $\textit{sgut-majorized}$ by $y$, and we write  $ x
    \prec_{sgut}y$  if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $x=Ry$. Define the relation $\sim_{sgut}$ as follows. $x\sim_{sgut}y$ if and only if $x$ is   sgut-majorized  by $y$ and $y$ is sgut-majorized  by $x$.  This paper characterizes all (strong)  linear preservers   of  $\sim_{sgut}$ on $\mathbb{R}^{n}$.

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References

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History

  • Receive Date: 15 June 2022
  • Revise Date: 17 September 2022
  • Accept Date: 25 November 2022

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