Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LINEAR RANK PRESERVERS ON INFINITE TRIANGULAR MATRICES

  • SLOWIK, ROKSANA (INSTITUTE OF MATHEMATICS SILESIAN UNIVERSITY OF TECHNOLOGY)
  • Received : 2014.08.08
  • Published : 2016.01.01
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Abstract

We consider ${\mathcal{T}}_{\infty}(F)$ - the space of all innite upper triangular matrices over a eld F. We give a description of all linear maps that satisfy the property: if rank(x) = 1, then $rank({\phi}(x))=1$ for all $x{\in}{\mathcal{T}}_{\infty}(F)$. Moreover, we characterize all injective linear maps on ${\mathcal{T}}_{\infty}(F)$ such that if rank(x) = k, then $rank({\phi}(x))=k$.

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References

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