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We consider $\mc T_\infty(F)$ -- the space of all infinite upper triangular matrices over a field $F$. We give a description of all linear maps that satisfy the property: if $\rank(x)=1$, then $\rank(\phi(x))=1$ for all $x\in\mc T_\infty(F)$. Moreover, we characterize all injective linear maps on $\mc T_\infty(F)$ such that if $\rank(x)=k$, then $\rank(\phi(x))=k$.
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참고문헌 (18)
참고문헌 신청
L. B. Beasley / 1981 / Linear transformations which preserve fixed rank / Linear Algebra Appl 40:183~187
L. B. Beasley / 1983 / Rank-k-preservers and preservers of sets of ranks / Linear Algebra Appl 55:11~17
L. B. Beasley / 1990 / Linear operators on matrices: the invariance of rank-k matrices / Linear Algebra Appl 133:175~184
L. B. Beasley / 1993 / Erratum: “Linear operators on matrices: the invariance of rank-k matrices” / Linear Algebra Appl 180(2)
J. Bell / 2000 / Additive rank-one preserving mappings on triangular matrix algebras / Linear Algebra Appl 312(1-3):13~33
L. B. Beasley / 1983 / Rank-k-preservers and preservers of sets of ranks / Linear Algebra Appl 55:11~17
L. B. Beasley / 1990 / Linear operators on matrices: the invariance of rank-k matrices / Linear Algebra Appl 133:175~184
L. B. Beasley / 1993 / Erratum: “Linear operators on matrices: the invariance of rank-k matrices” / Linear Algebra Appl 180(2)
J. Bell / 2000 / Additive rank-one preserving mappings on triangular matrix algebras / Linear Algebra Appl 312(1-3):13~33
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