{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-I7KE19CT/c660277792b30ee4fb880cfcf-943-3-42e-/PDF","dcterms:extent":"631 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-I7KE19CT/886d28ab-5744-4180-838d-99b9fcfdb14e/TEXT","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-I7KE19CT/9c02ed8c-949c-4036-a8bd-522e3eb25eb0/WEB","dcterms:extent":"0 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-I7KE19CT","dcterms:issued":"2014","dc:contributor":"Bračič, Janko","dc:creator":"Rudolf, Tina","dc:format":{"@xml:lang":"sl","#text":"XII, 73 str., 30 cm"},"dc:identifier":["COBISSID:16915545","PID:https://repozitorij.uni-lj.si/IzpisGradiva.php?id=95852","URN:URN:NBN:SI:doc-I7KE19CT"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"T. Rudolf"},"dc:source":{"@xml:lang":"sl","#text":"visokošolska dela"},"dc:subject":[{"@xml:lang":"sl","#text":"Disertacije"},{"@xml:lang":"sl","#text":"elementarni operatorji"},{"@xml:lang":"sl","#text":"elementary operators"},{"@xml:lang":"sl","#text":"generalized derivation"},{"@xml:lang":"sl","#text":"k-hiperrefleksivnost"},{"@xml:lang":"sl","#text":"k-hiperrefleksivnostna konstanta"},{"@xml:lang":"sl","#text":"k-hyperreflexivity"},{"@xml:lang":"sl","#text":"k-hyperreflexivity constant"},{"@xml:lang":"sl","#text":"k-refleksivno pokritje"},{"@xml:lang":"sl","#text":"k-refleksivnost"},{"@xml:lang":"sl","#text":"k-refleksivnostni defekt"},{"@xml:lang":"sl","#text":"k-reflexive cover"},{"@xml:lang":"sl","#text":"k-reflexivity"},{"@xml:lang":"sl","#text":"k-reflexivity defect"},{"@xml:lang":"sl","#text":"Kronecker canonical form"},{"@xml:lang":"sl","#text":"Kroneckerjeva kanonična forma."},{"@xml:lang":"sl","#text":"matrični šopi"},{"@xml:lang":"sl","#text":"matrix pencils"},{"@xml:lang":"sl","#text":"posplošeno odvajanje"},{"@xml:lang":"sl","#text":"Refleksivnost (matematika)"}],"dc:title":{"@xml:lang":"sl","#text":"Refleksivnost in refleksivnostni defekt prostorov operatorjev| doktorska disertacija|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$\\mathscr{H}$ ?be a complex separable Hilbert space, let ?$\\mathscr{B(H)}$? denote the algebra of all bounded linear operators on ?$\\mathscr{H}$? and let ?$k$? be a positive integer. Given a sequence of nonnegative integers ?$r_1 \\ge r_2 \\ge \\dots \\ge 0$? we show that there exists a subspace ?$\\mathcal{S} \\subseteq \\mathscr{B(H)}$?, such that its ?$k$?-reflexivity defect is equal to ?$r_k$? for all ?$k \\ge 1$?. For a finite dimensional complex Hilbert space we give an explicit formula for the reflexivity defect of the kernel of an arbitrary elementary operator of length 2, i.e., an operator, acting on the algebra ?$\\mathscr{B(H)}$?, of the form ?$\\Delta(T) = A_1TB_1 - A_2TB_2$? where ?$A_1$?, ?$A_2$? and ?$B_1$, $B_2$? are given pairs of linearly independent operators. We characterize the ?$k$?-reflexivity defect of the image of a generalized derivation. Using the latter we also give an explicit formula for the ?$k$?-reflexivity defect of the image of an elementary operator on ? $\\mathscr{B(H)}$? of the form ?$\\Delta(T) = ATB - T$? where ?$A, \\: B \\in \\mathscr{B(H)}$? are given operators. We also consider the ?$k$?-reflexivity and the $k$-hyperreflexivity of some subspaces of operators over the orthogonal direct sum of complex separable Hilbert spaces. We give a lower and upper bound for the $k$-hyperreflexivity constant of such a space and we prove that the lower bound is optimal. Furthermore, we give similar estimates when the direct sum of Hilbert spaces is not necessary orthogonal. In this case the bounds for the ?$k$?-hyperreflexivity constant depend also on the angles between the given Hilbert spaces. We also consider the hyperreflexivity constant of the low dimensional algebras of matrices that have a noncommutative lattice of invariant subspaces"},{"@xml:lang":"sl","#text":"Naj bo ?$\\mathscr{H}$? kompleksen separabilen Hilbertov prostor, ?$\\mathscr{B(H)}$? algebra omejenih linearnih operatorjev na ?$\\mathscr{H}$? in ?$k$? naravno število. Za dano zaporedje nenegativnih celih števil ?$r_1 \\ge r_2 \\ge \\dots \\ge 0$? dokažemo, da obstaja takšen podprostor ?$\\mathcal{S} \\subseteq \\mathscr{B(H)}$?, da je njegov ?$k$?-refleksivnostni defekt enak ?$r_k$? za vse ?$k \\ge 1$?. V primeru, ko je dani Hilbertov prostor končno razsežen, podamo eksplicitno formulo za refleksivnostni defekt jedra poljubnega elementarnega operatorja dolžine 2, t.j., operatorja na algebri ?$\\mathscr{B(H)}$? oblike ?$\\Delta(T) = A_1TB_1 - A_2TB_2$?, kjer sta ?$A_1$?, ?$A_2$? ter ?$B_1$?, ?$B_2$? para linearno neodvisnih operatorjev. Natančno karakteriziramo ?$k$?-refleksivnostni defekt slike posplošenega odvajanja ter slike elementarnega operatorja oblike ?$\\Delta(T) = ATB - T$?, kjer sta ?$A, \\: B \\in \\mathscr{B(H)}$? dana operatorja. Obravnavamo tudi ?$k$?-refleksivnost in ?$k$?-hiperrefleksivnost nekaterih prostorov operatorjev nad končno ortogonalno direktno vsoto kompleksnih separabilnih Hilbertovih prostorov. Poiščemo zgornjo in spodnjo mejo za ?$k$?-hiperrefleksivnostno konstanto takšnega prostora in pri tem dokažemo, da je dobljena spodnja meja optimalna. Podobne ocene izpeljemo tudi v primeru, ko direktna vsota Hilbertovih prostorov ni nujno ortogonalna. Izkaže se, da so dobljene meje za ?$k$?-hiperrefleksivnostno konstanto prostora tedaj odvisne tudi od kotov med danimi Hilbertovimi prostori. Obravnavamo še hiperrefleksivnostne konstante nizko razsežnih algeber matrik, ki imajo nekomutativno mrežo invariantnih podprostorov"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"visokošolska dela"},{"@xml:lang":"en","#text":"theses and dissertations"},{"@rdf:resource":"http://www.wikidata.org/entity/Q1266946"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:DOC-I7KE19CT","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-I7KE19CT"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-I7KE19CT/c660277792b30ee4fb880cfcf-943-3-42e-/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza v Ljubljani, Fakulteta za matematiko in fiziko"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-I7KE19CT/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-I7KE19CT"}}}}