1. 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: 20
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2. On certain functional equation arising from (m, n)-Jordan centralizers in prime ringsNina Peršin, Joso Vukman, 2012, original scientific article Abstract: The purpose of this paper is to prove the following result. Let ▫$m ge 1$▫, ▫$n ge 1$▫ be some fixed integers and let ▫$R$▫ be a prime ring with ▫$text{char}(R)= 0$▫ or ▫$(m+n)^2 < text{char}(R)$▫. Suppose there exists an additive mapping ▫$T colon R to R$▫ satisfying the relation ▫$2(m+n)^2T(x^3) = m(2m+n)T(x)x^2 + 2mnxT(x)x + n(2n+m)x^2T(x)$▫ for all ▫$x in R$▫. In this case ▫$T$▫ is a two-sided centralizer.
Keywords: matematika, algebra, kolobar, prakolobar, polprakolobar, Banachov prostor, Hilbertov prostor, algebra vseh omejenih linearnih operatorjev, standardna operatorska algebra, odvajanje, jordansko odvajanje, centralizator, algebra, ring, prime ring, semiprime ring, Banach space, Hilbert space, algebra of all bounded linear operators, standard operator algebra, derivation, Jordan derivation, left (right) centralizer, two-sided centralizer, left (right) Jordan centralizer, (m, n)-Jordan centralizer
Published in DKUM: 10.07.2015; Views: 1422; Downloads: 139
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3. Zero product determined algebrasMateja Grašič, 2011, published scientific conference contribution abstract Keywords: matematika, linearna algebra, algebra, določena z ničelnim produktom, matrična algebra, mathematics, linear algebra, zero product determined algebra, matrix algebra
Published in DKUM: 10.07.2015; Views: 1937; Downloads: 52
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4. On bilinear maps determined by rank one idempotentsJ. Alaminos, Matej Brešar, J. Extremera, A. R. Villena, 2009, original scientific article Abstract: Naj bo ▫$M_n$▫, ▫$n geqslant 2$▫, algebra vseh ▫$n times n$▫ matrik nad poljem ▫$F$▫ karakteristike različne od 2, in naj bo ▫$Phi$▫ bilinearna preslikava iz ▫$M_n times M_n$▫ v poljubni vektorski prostor ▫$X$▫ nad ▫$F$▫. Glavni izrek pove,da je iz pogoja, da je ▫$phi(e, f ) = 0$▫ za vse ortogonalne idempotente ▫$e$▫ in ▫$f$▫ ranga 1 sledi eksistenca linearnih takih preslikav ▫$Phi_1,Phi_2 colon M_n to X$▫, da je ▫$phi(a,b) = Phi_1(ab) + Phi_2(ba)$▫ za vse ▫$a,b in M_n$▫. Izrek se uporabi pri študiju nekaterih problemov o linearnih ohranjevalcih.
Keywords: matematika, teorija matrik, matrična algebra, ničelni produkt, idempotent ranga 1, linearna preslikava, bilinearna preslikava, linearni ohranjevalci, mathematics, matrix theory, matrix algebra, zero product, rank one idempotent, linear map, bilinear map, linear preserver problem
Published in DKUM: 10.07.2015; Views: 1672; Downloads: 99
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5. Hou, Jinchuan; Cui, Jianlian: Rank-1 preserving linear maps on nest algebras. (English). - [J] Linear Algebra Appl. 369, 263-277 (2003). [ISSN 0024-3795]Matej Brešar, 2005, review, book review, critique Keywords: matematika, teorija operatorjev, gnezdna algebra, lokalni avtomorfizmi, linearni ohranjevalci, mathematics, operator theory, rank-1 preserving maps, nest algebra, linear preservers, local automorphisms
Published in DKUM: 10.07.2015; Views: 2061; Downloads: 26
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6. Cui, Jianlian; Hou, Jinchuan: Linear maps preserving the closure of numerical range on nest algebras with maximal atomic nest. (English). - [J] Integral Equations Oper. Theory 46, No.3, 253-266 (2003). [ISSN 0378-620X]Matej Brešar, 2005, review, book review, critique Keywords: matematika, teorija operatorjev, numerični zaklad, gnezdna algebra, linearni ohranjevalec, mathematics, operator theory, numerical range, nest algebra, linear preserver
Published in DKUM: 10.07.2015; Views: 1163; Downloads: 23
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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: 28
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