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https://doi.org/10.3336/gm.47.1.07

On functional equations related to derivations in semiprime rings and standard operator algebras

Nejc Širovnik ; Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 Maribor, Slovenia

Puni tekst: engleski, pdf (105 KB) str. 95-104 preuzimanja: 249* citiraj
APA 6th Edition
Širovnik, N. (2012). On functional equations related to derivations in semiprime rings and standard operator algebras. Glasnik matematički, 47 (1), 95-104. https://doi.org/10.3336/gm.47.1.07
MLA 8th Edition
Širovnik, Nejc. "On functional equations related to derivations in semiprime rings and standard operator algebras." Glasnik matematički, vol. 47, br. 1, 2012, str. 95-104. https://doi.org/10.3336/gm.47.1.07. Citirano 17.10.2021.
Chicago 17th Edition
Širovnik, Nejc. "On functional equations related to derivations in semiprime rings and standard operator algebras." Glasnik matematički 47, br. 1 (2012): 95-104. https://doi.org/10.3336/gm.47.1.07
Harvard
Širovnik, N. (2012). 'On functional equations related to derivations in semiprime rings and standard operator algebras', Glasnik matematički, 47(1), str. 95-104. https://doi.org/10.3336/gm.47.1.07
Vancouver
Širovnik N. On functional equations related to derivations in semiprime rings and standard operator algebras. Glasnik matematički [Internet]. 2012 [pristupljeno 17.10.2021.];47(1):95-104. https://doi.org/10.3336/gm.47.1.07
IEEE
N. Širovnik, "On functional equations related to derivations in semiprime rings and standard operator algebras", Glasnik matematički, vol.47, br. 1, str. 95-104, 2012. [Online]. https://doi.org/10.3336/gm.47.1.07

Sažetak
In this paper functional equations related to derivations on semiprime rings and standard operator algebras are investigated. We prove, for example, the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) ⊂ L(X) be a standard operator algebra. Suppose there exist linear mappings D,G:A(X) → L(X) satisfying the relations D(A3)=D(A2)A+A2G(A),G(A3)=G(A2)A+A2D(A) for all A A(X). In this case there exists B L(X) such that D(A)=G(A)=[A,B] holds for all A A(X).

Ključne riječi
Prime ring; semiprime ring; Banach space; standard operator algebra; derivation; Jordan derivation; Jordan triple derivation

Hrčak ID: 82573

URI
https://hrcak.srce.hr/82573

Posjeta: 467 *