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
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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
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