ODVAJANJA NA KOLOBARJIH IN OPERATORSKIH ALGEBRAH

Širovnik, Nejc

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Title:	ODVAJANJA NA KOLOBARJIH IN OPERATORSKIH ALGEBRAH
Authors:	ID Širovnik, Nejc (Author) ID Vukman, Joso (Mentor) More about this mentor...
Files:	UNI_Sirovnik_Nejc_2010.pdf (508,46 KB) MD5: F26EE89B279864CE34891A71418EA32E
Language:	Slovenian
Work type:	Undergraduate thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V prvem delu diplomske naloge se seznanimo s strukturama prakolobar in polprakolobar. Na kolobarju vpeljemo pojme odvajanje, jordansko odvajanje ter jordansko trojno odvajanje. I. N. Herstein je leta 1957 dokazal, da je na prakolobarju brez elementov reda dva vsako jordansko odvajanje tudi odvajanje. V diplomski nalogi 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 polprakolobarje 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 polprakolobarju brez elementov reda dva tudi odvajanje. V diplomski nalogi najdemo dokaz tega izreka s krepkejšimi predpostavkami. Predstavljena sta tudi nova rezultata, ki spominjata na prej omenjen Brešarjev rezultat. Drugi del diplomske naloge 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 tudi različne posplošitve tega rezultata.
Keywords:	kolobar, prakolobar, polprakolobar, operatorska algebra, odvajanje, jordansko odvajanje, jordansko trojno odvajanje.
Place of publishing:	Maribor
Publisher:	[N. Širovnik]
Year of publishing:	2010
PID:	20.500.12556/DKUM-15083
UDC:	51(043.2)
COBISS.SI-ID:	17854216
NUK URN:	URN:SI:UM:DK:TTLWAUT9
Publication date in DKUM:	11.11.2010
Views:	2691
Downloads:	196
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	DERIVATIONS ON RINGS AND OPERATOR ALGEBRAS
Abstract:	The first part of the Graduation Thesis introduces prime and semiprime rings. On arbitrary ring concepts as derivation, Jordan derivation and Jordan triple derivation are defined. In year 1957 I. N. Herstein proved that every Jordan derivation on 2-torsion free prime ring is also a derivation. In the Thesis we present the alternative proof of this theorem, which was published by M. Brešar and J. Vukman in 1988. In year 1975 J. Cusack generalized Herstein's theorem on 2-torsion free semiprime rings. We present the proof of this theorem, which was published by M. Brešar in 1988. One year later he also proved that every Jordan triple derivation on 2-torsion free semiprime ring is a derivation as well. In the Thesis we present the proof of this theorem with some stronger assumptions. At the end of the first part two new results, motivated by Brešar's theorem, are proved. In the second part of the Thesis some results from functional analysis are proved. We present a classical result of P. R. Chernoff, concerning linear derivations on standard operator algebras of real or complex Banach space. We also meet some generalizations of Chernoff's result.
Keywords:	ring, prime ring, semiprime ring, operator algebra, derivation, Jordan derivation, Jordan triple derivation.

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