1434 KB22600 KB288 KB1982Lampret, VitoVidav, Ivan136 straniVIII, 126 f., 30 cmCOBISSID:6250501URN:URN:NBN:SI:doc-MA4U81UIslV. Lampretvisokošolska delaArbeidsgiverforeningen SpekterBanachove algebredisipativni elementienotafunkcionalna analizahermitski elementinormalni elementinormirane algebrenumerični radijnumerični zakladpoševno-hermitski elementipozitivni elementiprojektorjispekterspektralni radijSpekter in numerični zaklad elementa realne ali kompleksne normirane algebre (brez enote)| disertacija|The work deals with spectrum and algebra numerical range of an element of real or complex normed algebra which may be without a unit. It describes the relationship between spectrum and numerical range and characterizes skew-hermitian elements of a real algebra as well as hermitian and positive elements of a complex normed algebra. Hermitian and ?$^\ast$?-hermitian elements are treated with respect to involutive normed algebras. The attention is drawn to the properties of all the above mentioned elements and also to normal elements of a complex normed algebra. The main tool in this work is the complexification of real algebra and the non-standard adjunction of a unit to a normed algebra. The given examples explain relations between spectrum and numerical range and show certain irregularities which may occur in connection with spectrum, numerical range and hermitian elements. This may happen in case an algebra is without a unit or the norm of an eventual unit is ?$\ne 1$?. There exist for example a complex associative commutative ?$B$?-algebra without a unit including a sequence ?$h_n$? of hermitian elements such that ?$\|\sin h_n\| > n \; (n\in \NN)$?Delo obravnava spekter in numerični zaklad realne ali kompleksne normirane algebre, ki je lahko tudi brez enote, a je večinoma asociativna. Opisan je odnos med spektrom in numeričnim zakladom, ter med spektralnim radijem, numeričnim radijem in normo. Študirane so lastnosti poševno-hermitskih in hermitskih elementov ter pozitivnih in normalnih alementov. Obravnavana je algebrska stuktura linearnega prostora ?$H(A) + IH(A)$? ter njegova povezava z involutivnimi normiranimi algebrami. Na koncu je dodanih nekaj preprostih primerov, ki osvetlijo spekter in numerični zaklad elementa kompleksne oz. realne asociativne ?$B$?-algebre. Ti primeri tudi pokažejo kakšne anomalije v zvezi z numeričnim zakladom lahko nastopajo v kompleksni asociativni normirani algebri, ki ima lahko enoto ali pa je brez njedoktorska disertacijaTEXTvisokošolska delatheses and dissertationsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Ljubljani, Naravoslovnotehniška fakulteta