Proyecciones, ( ISI ), Volume (29), No (2), Year (2010-8) , Pages (101-108)

Title : ( JEWELL THEOREM FOR HIGHER DERIVATIONS ON C∗-ALGEBRAS )

Authors: Shirin Hejazian , Madjid Mirzavaziri , ,

Citation: BibTeX | EndNote

JEWELL THEOREM FOR HIGHER DERIVATIONS ON C∗-ALGEBRAS Let A be an algebra. A sequence {d_n} of linear mappings on A is called a higher derivation if dn(ab) = sum_{j=0}^n d_j(a)d_{n−j}(b) for each a, b ∈ A and each nonnegative integer n. Jewell [Pacific J. Math. 68 (1977), 91-98], showed that a higher derivation from a Banach algebra onto a semisimple Banach algebra is continuous provided that ker(d_0) ⊆ ker(d_m), for all m>=1. In this paper, under a different approach using C∗-algebraic tools, we prove that each higher derivation {d_n} on a C∗-algebra A is automatically continuous, provided that it is normal, i. e. d_0 is the identity mapping on A.

Keywords

, Derivation, higher derivation, automatic continuity, Sakai
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@article{paperid:1016719,
author = {Hejazian, Shirin and Mirzavaziri, Madjid and , },
title = {JEWELL THEOREM FOR HIGHER DERIVATIONS ON C∗-ALGEBRAS},
journal = {Proyecciones},
year = {2010},
volume = {29},
number = {2},
month = {August},
issn = {0716-0917},
pages = {101--108},
numpages = {7},
keywords = {Derivation; higher derivation; automatic continuity; Sakai theorem.},
}

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%0 Journal Article
%T JEWELL THEOREM FOR HIGHER DERIVATIONS ON C∗-ALGEBRAS
%A Hejazian, Shirin
%A Mirzavaziri, Madjid
%A ,
%J Proyecciones
%@ 0716-0917
%D 2010

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