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## Annales Mathematicae Silesianae

2019 | 33 | 97--105
Tytuł artykułu

### Left Derivable Maps at Non-Trivial Idempotents on Nest Algebras

Autorzy
Warianty tytułu
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)
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PL
EN
Czasopismo
Rocznik
Tom
Strony
97--105
Opis fizyczny
Twórcy
autor
• Department of Mathematics University of Kurdistan
autor
• Department of Mathematics University of Kurdistan
Bibliografia
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