Show document

A- | A+ | Print
Title:Mappings that preserve pairs of operators with zero triple Jordan product
Authors:Lešnjak, Gorazd (Author)
Petek, Tatjana (Author)
Li, Chi-Kwong (Author)
Kuzma, Bojan (Author)
Dobovišek, Mirko (Author)
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
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.
Keywords:matrix algebra, Jordan triple product, nonlinear preservers
Year of publishing:2007
Number of pages:str. 255-279
Numbering:Vol. 426, iss. 2-3
COBISS_ID:11598870 Link is opened in a new window
Categories:Document is not linked to any category.
Average score:(0 votes)
Your score:Voting is allowed only to logged in users.
Share:Bookmark and Share

Hover the mouse pointer over a document title to show the abstract or click on the title to get all document metadata.

Secondary language

Title:Preslikave, ki ohranjajo ničle produkta Jordanskih trojic
Abstract:Bodi ▫$\mathbb{F}$▫ komutativni obseg in ▫$n \ge 3$▫. Denimo, da ▫${\mathfrak{G_1,G_2}} \subseteq M_n(\mathbb{F})$▫ vsebuje vsaj vse idempotente ranga ena. V članku klasificiramo surjekcije ▫$\phi : \mathfrak{G_1} \to \mathfrak{G_2}$▫ z lastnostjo ▫$ABA = 0 \iff \phi(A)\phi(B)\phi(A) = 0$▫. Klasificiramo tudi sorodne preslikave na (a) podmnožicah omejenih operatorjev na Banachovem prostoru, (b) podmnožicah Hermitskih matrik s koeficienti iz (nenujno komutativnega) obsega, (c) podmnožicah sebi-adjungiranih operatorjev na neskončnorazsežnem, kompleksnem Hilbertovem prostoru. Dobljene rezultate lahko apliciramo npr. pri iskanju preslikav ▫$\phi$▫, z lastnostjo ▫$F(ABA) = F(\phi(A)\phi(B)\phi(A))$▫ kjer se ▫$F$▫ unitarno-podobnostno-invariantne funkcije, kot npr. spektralna norma, Schattenova ▫$p$▫-norma, numerični zaklad, numerični radij, itd.
Keywords:matematika, matrična algebra, produkt jordanskih trojic, nelinearni ohranjevalci


Leave comment

You have to log in to leave a comment.

Comments (0)
0 - 0 / 0
There are no comments!

Logos of partners University of Maribor University of Ljubljana University of Primorska University of Nova Gorica