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A non-smooth extension of Frechet differentiability of the norm with applications to numerical ranges

Published online by Cambridge University Press:  18 May 2009

C. Aparicio ,
F. Ocaña ,
R. Payá  and
A. Rodríguez
C. Aparicio
Affiliation:
Departamento de Teoria de Funciones, Facultad de Ciencias, Universidad de Granada, Spain
F. Ocaña
Affiliation:
Departamento de Teoria de Funciones, Facultad de Ciencias, Universidad de Granada, Spain
R. Payá
Affiliation:
Departamento de Teoria de Funciones, Facultad de Ciencias, Universidad de Granada, Spain
A. Rodríguez
Affiliation:
Departamento de Teoria de Funciones, Facultad de Ciencias, Universidad de Granada, Spain
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The following result in the theory of numerical ranges in Banach algebras is well known (see [3, Theorem 12.2]). The numerical range of an element F in the bidual of a unital Banach algebra A is the closure of the set of values at F of the w*-continuous states of . As a consequence of the results in this paper the following

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 121 - 137
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

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