20.500.12556/RUP-2200 Jordan [tau]-derivations of locally matrix rings Let ▫$R$▫ be a prime, locally matrix ring of characteristic not 2 and let ▫$Q_{ms}(R)$▫ be the maximal symmetric ring of quotients of ▫$R$▫. Suppose that ▫$\delta \colon R \to Q_{ms}(R)$▫ is a Jordan ▫$\tau$▫-derivation, where ▫$\tau$▫ is an anti-automorphism of $R$. Then there exists ▫$a \in Q_{ms}(R)$▫ such that ▫$\delta(x) = xa - a\tau(x)$▫ for all ▫$x \in R$▫. Let ▫$X$▫ be a Banach space over the field ▫$\mathbb{F}$▫ of real or complex numbers and let ▫$\mathcal{B}(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫. We prove that ▫$Q_{ms}(\mathcal{B}(X)) = \mathcal{B}(X)$▫, which provides the viewpoint of ring theory for some results concerning derivations on the algebra ▫$\mathcal{B}(X)$▫. In particular, all Jordan ▫$\tau$▫-derivations of ▫$\mathcal{B}(X)$▫ are inner if ▫$\dim_{\mathbb{F}} X>1$▫. Naj bo ▫$R$▫ lokalno matrični prakolobar s karakteristiko različno od 2 in ▫$Q_{ms}(R)$▫ maksimalni simetrični kolobar kvocientov kolobarja ▫$R$▫. Naj bo ▫$\delta \colon R \to Q_{ms}(R)$▫ jordansko ▫$\tau$▫-odvajanje, kjer je ▫$\tau$▫ antiavtomorfizem kolobarja ▫$R$▫. Potem obstaja tak ▫$a \in Q_{ms}(R)$▫, da je ▫$\delta(x) = xa - a\tau(x)$▫ za vse ▫$x \in R$▫. Naj bo ▫$X$▫ Banachov prostor nad kompleksnim ali realnim poljem ▫$\mathbb{F}$▫ in ▫$\mathcal{B}(X)$▫ algebra omejenih linearnih operatorjev na ▫$X$▫. V članku je dokazano, da je ▫$Q_{ms}(\mathcal{B}(X)) = \mathcal{B}(X)$▫. mathematics algebra anti-automorphism locally matrix ring prime ring Jordan homomorphism Jordan ▫$\tau$▫-derivation Banach space matematika algebra antiavtomorfizem lokalno matrični kolobar prakolobar jordanski homomorfizem jordansko ▫$\tau$▫-odvajanje Banachov prostor true true false Angleški jezik Slovenski jezik Delo ni kategorizirano 2013-10-15 12:06:53 2013-10-15 12:06:53 2024-03-01 12:03:18 0000-00-00 00:00:00 2013 0 0 str. 755-763 iss. 3 Vol. 16 2013 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1386-923X 512.552 16195673 http://dx.doi.org/10.1007/s10468-011-9329-8 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=2200 Inštitut Andrej Marušič 0 0 0