20.500.12556/DKUM-18907 Komutirajoče preslikave trikotnih algeber Commuting maps of triangular algebras V diplomskem delu definiramo pojem trikotne algebre. Dokažemo nekatere osnovne lastnosti in podamo osnovne primere trikotnih algeber, med katerimi sta najpomembnejši algebra zgornje trikotnih matrik Tn(R) in gnezdna algebra T(N). V nadaljevanju se ukvarjamo s komutirajočimi preslikavami trikotnih algeber. Preslikava f algebre A je komutirajoča, če velja f(a)a = af(a) za vsak a ∈ A. Zanima nas oblika komutirajoče linearne preslikave trikotne algebre. Glavni cilj tretjega poglavja je poiskati tak razred trikotnih algeber, katerih vse komutirajoče linearne preslikave imajo standardno obliko. Proučujemo tudi komutirajočo sled poljubne bilinearne preslikave B : U × U → U trikotne algebre U. Zanima nas oblika preslikave x → B(x, x), ki zadošča pogoju B(x, x)x−xB(x, x) = 0 za vsak x ∈ U. Naš cilj je poiskati tak razred trikotnih algeber, katerih vse komutirajoče sledi bilinearnih preslikav imajo standardno obliko. In the graduation thesis the notion of a triangular algebra is introduced. We derive some of their basic properties and present classical examples of triangular algebras, among which the upper triangular matrix algebra Tn(R) and nest algebra T(N) are the most important. We proceed to study commuting maps of triangular algebras. A map f of an algebra A is called a commuting map if f(a)a = af(a) for every a ∈ A. We consider the form of a commuting map of a triangular algebra. The main purpose of the third chapter is to identify a class of triangular algebras for which every commuting linear map is proper. We also study a commuting trace of an arbitrary bilinear map B : U × U → U on a triangular algebra U. We consider the form of a map x → B(x, x), which satisfies the condition B(x, x)x − xB(x, x) = 0 for every x ∈ U. Our main purpose is to identify a certain class of triangular algebras for which every commuting trace of a bilinear map is proper. Trikotna algebra algebra zgornje trikotnih matrik gnezdna algebra komutirajoča preslikava komutirajoča sled bilinearne preslikave. Triangular algebra upper triangular matrix algebra nest algebra commuting map commuting trace of a bilinear map. true true false [B. Trebežnik] Slovenski jezik Angleški jezik Diplomsko delo 2011-06-08 17:57:19 2011-07-07 12:59:09 2022-04-13 14:55:07 2023-12-24 03:27:50 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18504712 URN:SI:UM:DK:MM2IROKV UNI_Trebeznik_Bojan_2011.pdf UNI_Trebeznik_Bojan_2011.pdf 1 861FCBCAFD53D38B3FBF852357B042FD 5338540405dd0adae5a9f5bc57f1152689d036ea75a262dbcbe5059259006f10 3f0b2eab-7c05-11eb-bb7a-00155d0001ca 20.500.12556/dkum/e12c6ab5-257c-4e35-ab89-57a9042af29d https://dk.um.si/Dokument.php?lang=slv&id=22652 Fakulteta za naravoslovje in matematiko 0 0 0