Left derivable maps at non-trivial idempotents on nest algebras

Hoger Ghahramani; Saman Sattari

Published: 2019-04-05

Vol. 33 (2019)

Left derivable maps at non-trivial idempotents on nest algebras

Hoger Ghahramani , Saman Sattari

Abstract

Let Alg N be a nest algebra associated with the nest N on a (real or complex) Banach space X. Suppose that there exists a non-trivial idempotent P∈Alg N with range P(X)∈?N, and δ:Alg N→Alg N is a continuous linear mapping (generalized) left derivable at P, i.e. δ(ab) = aδ(b) + bδ(a) (δ(ab) = aδ(b) + bδ(a) - baδ(I)) for any a,b∈Alg N with ab = P, where I is the identity element of AlgN. We show that δ is a (generalized) Jordan left derivation. Moreover, in a strongly operator topology we characterize continuous linear maps on some nest algebras Alg???? with the property that δ(P) = 2Pδ(P) or δ(P) = 2Pδ(P) - Pδ(I) for every idempotent P in Alg N.

Keywords:

nest algebra , left derivable , left derivation

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Ghahramani, H., & Sattari, S. (2019). Left derivable maps at non-trivial idempotents on nest algebras. Annales Mathematicae Silesianae, 33, 97–105. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13653

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