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Non-reflexivity of the derivation space from Banach algebras of analytic functions


Author: Ebrahim Samei
Journal: Proc. Amer. Math. Soc. 135 (2007), 2045-2049
MSC (2000): Primary 47B47, 13J07
DOI: https://doi.org/10.1090/S0002-9939-07-08655-8
Published electronically: February 28, 2007
MathSciNet review: 2299478
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Abstract: Let $ \Omega$ be an open connected subset of the plane, and let $ A$ be a Banach algebra of analytic functions on $ \Omega$. We show that the space of bounded derivations from $ A$ into $ A^*$ is not reflexive. We also obtain similar results when $ A=C^{(n)}[0,1]$ for $ n\geq 2$.


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Additional Information

Ebrahim Samei
Affiliation: EPFL-SB-IACS, Station 8, Ch-1015 Lausanne, Switzerland
Email: ebrahim.samei@epfl.ch

DOI: https://doi.org/10.1090/S0002-9939-07-08655-8
Keywords: Local derivations, reflexivity, analytic functions, differentiable functions
Received by editor(s): July 29, 2005
Received by editor(s) in revised form: January 30, 2006
Published electronically: February 28, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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