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Simultaneous zero inclusion property for spatial numerical rangesBračič, Janko ; Diogo, CristinaZa končno dimenzionalen kompleksen normiran prostor ▫$\mathscr{X}$▫ rečemo, da ima lastnost simultane vsebovanosti ničle, če ima obrnljiv operator ▫$S$▫ na ▫$\mathscr{X}$▫ ničlo v svojem prostorskem ... številskem zakladu vrednosti natanko tedaj, ko jo ima v svojem prostorskem številskem zakladu vrednosti tudi inverz operatorja ▫$S$▫. Pokažemo, da imajo to lastnost poleg Hilbertovih prostorov še nekateri drugi normirani prostori. Po drugi strani, prostor ▫$\ell_1(n)$▫ nima te lastnosti. Ker nima vsak normiran prostor omenjene lastnosti, raziščemo razred tistih operatorjev za katere ta lastnost velja. Na koncu obravnavamo lastnost, ki je močnejša od lastnost simultane vsebovanosti ničle za prostorske številske zaklade vrednosti in je povezana z vprašanjem, kdaj je mogoče, za vsak obrnljiv operator ▫$S$▫, kontrolirati oddaljenost $0$ do prostorskega številskega zaklada operatorja▫ $S^{-1}$▫ z oddaljenostjo števila ▫$0$▫ do prostorskega številskega zaklada operatorja ▫$S$▫.Source: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 449, iss. 2, 2017, str. 1413-1423)Type of material - article, component part ; adult, seriousPublish date - 2017Language - englishCOBISS.SI-ID - 18028633
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source: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 449, iss. 2, 2017, str. 1413-1423)
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Bračič, Janko | 19511 |
Diogo, Cristina | ![]() |
Source: Personal bibliographies
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