1. An identity with derivations on rings and Banach algebrasAjda Fošner, Maja Fošner, Joso Vukman, 2008, original scientific article Abstract: The main purpose of this paper is to study the following: Let m, n, and $k_{i}, i = 1, 2, ..., n$ be positive integers and let $R$ be a $2m(m+ k_{1} + k_{2} + ... + k_{n} -1)!$-torsion free semiprime ring. Suppose that there exist derivations $D_{i} : R \to R, i = 1, 2, ..., n + 1$ , such that $D_{1}(x^{m})x^{k_{1}+...+k_{n}}+x^{k_{1}} D_{2}(x^{m})x^{k_{2}+...+k_{n}}+...+x^{k_{1}+...+k_{n}}D_{n+1}(x^{m})=0$ holds for all $x \in R$. Then we prove that $D_{1}+D_{2}+...+D_{n+1}=0$ and that the derivation $k_{1}D_{2}+(k_{1}+k_{2})D_{3}+...+(k_{1}+k_{2}+...+k{n})D_{n+1}$ maps $R$ into its center. We also obtain a range inclusion result of continuous derivations on Banach algebras.
Keywords: mathematics, algebra, associative rings and algebras, prime rings, Banach algebras, identities, derivations
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2. Cui, Jianlian; Hou, Jinchuan: Linear maps on von Neumann algebras preserving zero products of tr-rank. (English). - [J] Bull. Aust. Math. Soc. 65, No.1, 79-91(2002). [ISSN 0004-9727]Matej Brešar, 2005, review, book review, critique Keywords: matematika, teorija operatorjev, linearni ohranjevalci, von Neumannove algebre, ničelni produkt, mathematics, operator theory, Banach algebras, linear preservers, von Neumann algebra, zero product, tr-rank
Published in DKUM: 16.07.2015; Views: 1380; Downloads: 25
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3. Lee, Tsiu-Kwen: Derivations on noncommutative Banach algebras. (English). - [J] Stud. Math. 167, No.2, 153-160 (2005). [ISSN 0039-3223; ISSN 1730-6337]Matej Brešar, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, odvajanje, kvazinilpotentnost, Banachova algebra, Jacobsonov radikal, prakolobar, polenostavni kolobarji, mathematics, operator theory, derivation, quasinilpotent, Banach algebra, Jacobson radical, prime ring, semisimple ring
Published in DKUM: 10.07.2015; Views: 1166; Downloads: 33
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4. Lyubich, Yu.: Banach-Bernstein algebras and their applications. (English). - [CA] Costa, Roberto (ed.) et al., Nonassociative algebra and its applications. Proceedings of the fourth international conference, Sao Paulo, Brazil. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 211, 205-210 (2000). [ISBN 0-8247-0406-1/pbk]Matej Brešar, 2004, review, book review, critique Keywords: matematika, algebra, neasociativne topološke algebre, integralski operatorji, Bernsteinovo jedro, Banach-Bernsteinova algebra, mathematics, algebra, nonassociative topological algebras, integral operators, Banach-Bernstein algebra, Bernstein kernel
Published in DKUM: 10.07.2015; Views: 967; Downloads: 37
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5. Hessenberger, Gerald: An improved characterization of inessential elements in Banach Jordan systems and the generalized Ruston characterization. (English). - [J] Arch. Math. 74, No.6, 438-440 (2000). [ISSN 0003-889X; ISSN 1420-8938]Matej Brešar, 2004, review, book review, critique Keywords: matematika, algebra, neasociativne topološke algebre, jordanske strukture, Banachov prostor, mathematics, algebra, nonassociative topological algebras, Jordan structures, Banach Jordan system, inessential element, Riesz element, quasi-Fredholm element
Published in DKUM: 10.07.2015; Views: 982; Downloads: 19
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6. On automorphisms of Banach algebrasMatej Brešar, 2002, original scientific article Abstract: Podana je razširitev Jacobsonovega izreka o gostoti na Banachove algebre z avtomorfizmi. Zatem so obravnave aplikacije tega izreka. Med drugim so karakterizirani avtomorfizmi ▫$alpha$▫ na Banachovi algebri z lastnostjo, da je preslikava ▫$alpha-1$▫ spektralno omejena.
Keywords: matematika, funkcionalna analiza, teorija operatorjev, avtomorfizem, Banachova algebra, izrek o gostoti, spektralno omejena preslikava, mathematics, functional analysis, operator theory, automorphism, Banach algebra, density theorem, spectrally bounded map
Published in DKUM: 10.07.2015; Views: 1286; Downloads: 115
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7. Commuting maps: a surveyMatej Brešar, 2004, review article Abstract: A map ▫$f$▫ on a ring ▫$mathcal{A}$▫ is said to be commuting if ▫$f(x)$▫ commutes with ▫$x$▫ for every ▫$x in mathcal{A}$▫. The paper surveys the development of the theory of commuting maps and their applications. The following topics are discussed: commuting derivations, commuting additive maps, commuting traces of multiadditive maps, various generalizations of the notion of a commuting map, and applications of results on commuting maps to different areas, in particular to Lie theory.
Keywords: matematika, algebra, prakolobar, komutirajoča preslikava, funkcijska identiteta, Banachova algebra, odvajanje, Liejeve algebre, linearni ohranjevalci, mathematics, algebra, commuting map, functional identity, prime ring, Banach algebra, derivation, Lie theory, linear preservers
Published in DKUM: 10.07.2015; Views: 1541; Downloads: 35
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8. Symmetric bi-derivations on prime and semi-prime ringsJoso Vukman, 1989, original scientific article Abstract: Naj bo ▫$K$▫ kolobar. Biaditivna simetrična preslikava ▫$D(.,.):K times K to K$▫ je simetrična biderivacija, če je za vsak fiksen ▫$y in K$▫ preslikava ▫$x mapsto D(x,y)$▫ derivacija. Glavni namen članka je dokazati rezultat v smislu klasičnega izreka E. Posnerja, ki pravi naslednje: Če je ▫$K$▫ prakolobar s karakteristiko različno od dva in sta ▫$D_1$▫ in ▫$D_2$▫ od nič različni derivaciji, potem preslikava ▫$x mapsto D_1(D_2(x))$▫ ne more biti derivacija.
Keywords: matematika, asociativni kolobarji in algebre, kolobar, prakolobar, polprakolobar, derivacija, simetrična biderivacija, mathematics, associative rings and algebras, prime ring, semiprime ring, derivation, simetric biderivation, semiprime ring, Banach algebra
Published in DKUM: 10.07.2015; Views: 1326; Downloads: 101
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9. Some functional equations in banach algebras and an applicationJoso Vukman, 1987, original scientific article Abstract: V članku so dokazani rezultati o neki funkcionalni enačbi v kompleksni Banachovi algebri. Eden teh rezultatov je uporabljen pri dokazu abstraktne posplošitve Jordan-Neumannove karakterizacije predhilbertovega prostora.
Keywords: matematika, funkcionalna analiza, Banachova algebra, Banachova ▫$ast$▫-algebra, vektorski prostor, modul, aditivna funkcija, avtomorfizem, antiavtomorfizem, prehilbertov prostor, mathematics, functional analysis, Banach algebra, Banach ▫$ast$▫-algebra, vector space, module, additive functions, automorphism, antiautomorphism, pre-Hilbert space
Published in DKUM: 10.07.2015; Views: 1384; Downloads: 100
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