| Title: | Mappings that preserve pairs of operators with zero triple Jordan product |
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| Authors: | ID Dobovišek, Mirko (Author)
ID Kuzma, Bojan (Author)
ID Lešnjak, Gorazd (Author)
ID Li, Chi-Kwong (Author)
ID Petek, Tatjana (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.laa.2007.04.017
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | Let ▫$\mathbb{F}$▫ be a field and ▫$n \ge 3$▫. Suppose ▫${\mathfrak{G_1,G_2}} \subseteq M_n(\mathbb{F})▫$ contain all rank-one idempotents. The structure of surjections ▫$\phi : \mathfrak{G_1} \to \mathfrak{G_2}$▫ satisfying ▫$ABA = 0 \iff \phi(A)\phi(B)\phi(A) = 0$▫ is determined. Similar results are also obtained for (a) subsets of bounded operators acting on a complex or real Banach space, (b) the space of Hermitian matrices acting on ▫$n$▫-dimensional vectors over a skew-field, (c) subsets of self-adjoint bounded linear operators acting on an infinite dimensional complex Hilbert space. It is then illustrated that the results can be applied to characterize mappings ▫$\phi$▫ on matrices or operators such that ▫$F(ABA) = F(\phi(A)\phi(B)\phi(A))▫$ for all ▫$A,B$▫ for functions ▫$F$▫ such as the spectral norm, Schatten ▫$p$▫-norm, numerical radius and numerical range, etc. |
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| Keywords: | matrix algebra, Jordan triple product, nonlinear preservers |
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| Year of publishing: | 2007 |
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| Number of pages: | str. 255-279 |
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| Numbering: | Vol. 426, iss. 2-3 |
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| PID: | 20.500.12556/RUP-7714  |
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| ISSN: | 0024-3795 |
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| UDC: | 512.552 |
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| COBISS.SI-ID: | 11598870 |
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| Publication date in RUP: | 03.04.2017 |
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| Views: | 2430 |
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| Downloads: | 97 |
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