| Title: | Jordan [tau]-derivations of locally matrix rings |
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| Authors: | ID Chuang, Chen-Lian (Author)
ID Fošner, Ajda (Author)
ID Lee, Tsiu Kwen (Author) |
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| Files: |  http://dx.doi.org/10.1007/s10468-011-9329-8
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | 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 ▫$\dim_{\mathbb{F}} X>1$▫. |
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| Keywords: | mathematics, algebra, anti-automorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫-derivation, Banach space |
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| Year of publishing: | 2013 |
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| Number of pages: | str. 755-763 |
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| Numbering: | Vol. 16, iss. 3 |
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| PID: | 20.500.12556/RUP-2200  |
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| ISSN: | 1386-923X |
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| UDC: | 512.552 |
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| COBISS.SI-ID: | 16195673 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 4952 |
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| Downloads: | 85 |
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