Linear preservers of rank k projections.
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| Title: | Linear preservers of rank k projections. |
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| Authors: | Plevnik, Lucijan1 (AUTHOR) lucijan.plevnik@fmf.uni-lj.si |
| Source: | Linear Algebra & its Applications. Aug2026, Vol. 742, p101-130. 30p. |
| Subjects: | Hilbert space, Selfadjoint operators, Linear operators, Unitary operators, Matrices (Mathematics) |
| Abstract: | Let H be a complex Hilbert space and F s (H) the real vector space of all self-adjoint finite rank bounded operators on H. We generalize the famous Wigner's theorem by characterizing linear maps on F s (H) which preserve the set of all rank k projections. In order to do this, we first characterize linear maps on the real vector space H 0 , 2 k of trace zero (2 k) × (2 k) hermitian matrices which preserve the subset of unitary matrices in H 0 , 2 k. We also study linear maps from F s (H) to F s (K) sending projections of rank k to finite rank projections. We prove some properties of such maps, e.g. that they send rank k projections to projections of a fixed rank. We give the complete description of such maps in the case dim H = 2. We give several examples which show that in the general case the problem to describe all such maps seems to be complicated. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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