Characterization of two-sided generalized derivations

Hosseini Amin: Characterization of two-sided generalized derivations. In: Acta scientiarum mathematicarum, (86) 3-4. pp. 577-600. (2020)

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Abstract

Let A be a unital semiprime, complex normed ∗-algebra and let f, g, h : A → A be linear mappings such that f and g+h are continuous. Under certain conditions, we prove that if f(p ◦ p) = g(p) ◦ p + p ◦ h(p) holds for any projection p of A, then f and g+h are two-sided generalized derivations, where a◦b = ab+ba. We present some consequences of this result. Moreover, we show that if A is a semiprime algebra with the unit element e and n > 1 is an integer such that the linear mappings f, g : A → A satisfy f(x n ) = Pn j=1 x n−j g(x)x j−1 for all x ∈ A and further g(e) ∈ Z(A), then f and g are two-sided generalized derivations associated with the same derivation. Also, we show that if A is a unital, semiprime Banach algebra and F, G: A → A are linear mappings satisfying F(b) = −bG(b −1 )b for all invertible elements b ∈ A, then F and G are two-sided generalized derivations. Some other related results are also discussed.

Item Type:	Article
Heading title:	Analysis
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2020
Volume:	86
Number:	3-4
ISSN:	2064-8316
Page Range:	pp. 577-600
Language:	English
Related URLs:	http://acta.bibl.u-szeged.hu/73790/
DOI:	10.14232/actasm-020-295-8
Uncontrolled Keywords:	Matematika
Additional Information:	Bibliogr.: p. 598-600. ; összefoglalás angol nyelven
Date Deposited:	2021. Nov. 15. 14:09
Last Modified:	2021. Nov. 15. 14:09
URI:	http://acta.bibl.u-szeged.hu/id/eprint/73905

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