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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

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 $rank({\phi}(x))=k$.

Keywords

References

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  1. Bilocal automorphisms of T ∞(F) vol.48, pp.3, 2017, https://doi.org/10.1007/s13226-017-0235-6