Italian Journal of Pure and Applied Mathematics, No (32), Year (2014-10) , Pages (595-602)

Title : ( A characterization of higher derivations on Banach algebras )

Authors: T.L. Shatery , Shirin Hejazian ,

Citation: BibTeX | EndNote

Let A be a Banach algebra and let every module-valued derivation from A to any Banach A-bimodule be continuous. We show that if {dm} is a higher derivation from A to a Banach algebra B with continuous d0, then there exist a continuous left A-module homomorphism U : B(A1; B) → B and a sequence {Dm} of module-valued derivations from A into B(A1; B) such that dm = U ◦Dm (m ≥ 1), and as a consequence {dm} is automatically continuous. We also obtain a partial result concerning innerness of higher derivations on W*-algebras.

Keywords

, derivation, higher derivation, intertwining map, inner
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@article{paperid:1046405,
author = {T.L. Shatery and Hejazian, Shirin},
title = {A characterization of higher derivations on Banach algebras},
journal = {Italian Journal of Pure and Applied Mathematics},
year = {2014},
number = {32},
month = {October},
issn = {1126-8042},
pages = {595--602},
numpages = {7},
keywords = {derivation; higher derivation; intertwining map; inner derivation},
}

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%0 Journal Article
%T A characterization of higher derivations on Banach algebras
%A T.L. Shatery
%A Hejazian, Shirin
%J Italian Journal of Pure and Applied Mathematics
%@ 1126-8042
%D 2014

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