Left Derivable Maps at Non-Trivial Idempotents on Nest Algebras

Czasopismo

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• Autorzy: Hoger Ghahramani , Saman Sattari
• Języki publikacji: EN

Abstrakty

EN

Let $Alg\mathcal{N}$ be a nest algebra associated with the nest $\mathcal{N}$ on a (real or complex) Banach space $\mathds{X}$. Suppose that there exists a non-trivial idempotent $P\in Alg\mathcal{N}$ with range $P(\mathds{X})\in\mathcal{N}$, and $\delta\colon Alg\mathcal{N}\to Alg\mathcal{N}$ is a continuous linear mapping (generalized) left derivable at $P$, i.e. $\delta(ab) = a\delta(b) + b\delta(a)$ $(\delta(ab) = a\delta(b) + b\delta(a) - ba\delta(I))$ for any $a,b\in Alg\mathcal{N}$ with $ab = P$, where $I$ is the identity element of $Alg\mathcal{N}$. We show that $\delta$ is a (generalized) Jordan left derivation. Moreover, in a strongly operator topology we characterize continuous linear maps $\delta$ on some nest algebras $Alg\mathcal{N}$ with the (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Mathematical statistics; Number theory

PL

Matematyka; Funkcje matematyczne; Statystyka matematyczna; Teoria liczb

• Czasopismo: ---
• Strony: 97--105

Twórcy

autor

Hoger Ghahramani

• Department of Mathematics University of Kurdistan

autor

Saman Sattari

• Department of Mathematics University of Kurdistan

Bibliografia

• F.F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, Berlin, 1973.
• M. Bre sar, Characterizations of derivations on some normed algebras with involution, J. Algebra 152 (1992), 454-462.
• M. Bre sar, Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. Roy. Soc. Edinburgh. Sect. A 137 (2007), 9-21.
• M. Bre sar and J. Vukman, On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1990), 7-16.
• K.R. Davidson, Nest Algebras, Pitman Res. Notes in Math., vol. 191, Longman, London, 1988.
• B. Fadaee and H. Ghahramani, Jordan left derivations at the idempotent elements on reflexive algebras, Publ. Math. Debrecen 92 (2018), 261-275.
• H. Ghahramani, Additive mappings derivable at non-trivial idempotents on Banach algebras, Linear Multilinear Algebra 60 (2012), 725-742.
• H. Ghahramani, On centralizers of Banach algebras, Bull. Malays. Math. Sci. Soc. 38 (2015), 155-164.
• H. Ghahramani, Characterizing Jordan maps on triangular rings through commutative zero products, Mediterr. J. Math. 15 (2018), Art. 38, 10 pp., DOI: 10.1007/s00009-018- 1082-3.
• N.M. Ghosseiri, On Jordan left derivations and generalized Jordan left derivations of matrix rings, Bull. Iranian Math. Soc. 38 (2012), 689-698.
• [J.C. Hou and X.L. Zhang, Ring isomorphisms and linear or additive maps preserving zero products on nest algebras, Linear Algebra Appl. 387 (2004), 343-360.
• J.K. Li and J. Zhou, Jordan left derivations and some left derivable maps, Oper. Matrices 4 (2010), 127-138.
• N.K. Spanoudakis, Generalizations of certain nest algebra results, Proc. Amer. Math. Soc. 115 (1992), 711-723.
• J. Vukman, On left Jordan derivations of rings and Banach algebras, Aequationes Math. 75 (2008), 260-266.
• B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32 (1991), 609-614.
• J. Zhu and C.P. Xiong, Derivable mappings at unit operator on nest algebras, Linear Algebra Appl. 422 (2007), 721-735.

Identyfikatory

DOI

10.2478/amsil-2019-0001