Odvajanja na kolobarjih in operatorskih algebrah : diplomsko delo

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Odvajanja na kolobarjih in operatorskih algebrah : diplomsko delo

Širovnik, Nejc

V prvem delu diplomskega dela se seznanimo s strukturama prakolobar in pol prakolobar. Na kolobarju vpeljemo pojme odvajanje, jordansko odvajanje in jordansko trojno odvajanje. I. N. Herstein je leta ... 1957 dokazal, da je na prakolobarju brez elementov reda dva vsako jordansko odvajanje tudi odvajanje. V diplomskem delu je predstavljen alternativni dokaz tega izreka, ki sta ga leta 1988 objavila M. Brešar in J. Vukman. J. Cusack je leta 1975 Hersteinov izrek posplošil na pol prakolobarje brez elementov reda dva. V diplomskem delu je predstavljen dokaz tega izreka, ki ga je leta 1988 objavil M. Brešar. M. Brešar je leta 1989 dokazal, da je vsako jordansko trojno odvajanje na pol prakolobarju brez elementov reda dva tudi odvajanje. V diplomskem delu najdemo dokaz tega izreka s krepkejšimi predpostavkami. Predstavljena sta tudi nova rezultata, ki spominjata na prej omenjen Brešarjev rezultat. Drugi del diplomskega dela sega na področje funkcionalne analize. Osnova je rezultat P. R. Chernoffa, ki govori o linearnih odvajanjih na standardnih operatorskih algebrah realnega ali kompleksnega Banachovega prostora. Predstavljene so različne posplošitve tega rezultata.

Type of material - undergraduate thesis ; adult, serious

Publication and manufacture - Maribor : [N. Širovnik], 2010

Language - slovenian

COBISS.SI-ID - 17854216

Link(s):
Digital Library of the University of Maribor – DLUM

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Library/institution	City	Acronym	For loan	Other holdings
Miklošič Library FPNM, Maribor	Maribor	PEFMB	reading room 1 cop.
University of Maribor Library	Maribor	UKM	reading room 1 cop.

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Year	Impact factor		Edition		Category		Classification
Year	JCR	SNIP	JCR	SNIP	JCR	SNIP	JCR	SNIP

Links to authors' personal bibliographies	Links to information on researchers in the SICRIS system
Širovnik, Nejc	33266
Vukman, Joso	04310

Source: Personal bibliographies and: SICRIS

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