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Density of numerical radius attaining operators on some reflexive spaces

Published online by Cambridge University Press:  17 April 2009

Carmen Silvia Cardassi
Carmen Silvia Cardassi
Affiliation:
Instituto de Matematica e Estatistica, Universidade de Sāo Paulo, C.P. 20570 (Ag. Iguatemi), 01498 - Sāo Paulo, Brasil.
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Abstract

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We show that for reflexive spaces X the density of numerical radius attaining operators in L(X) is equivalent to the density of numerical radius attaining operators in L(X*). As a consequence of this fact and of a result of Berg and Sims, we prove that for uniformly smooth spaces X the numerical radius attaining operators are dense in L(X).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 1 , February 1985 , pp. 1 - 3
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Berg, I.D. and Sims, Brailey, “Denseness of operators which attain their numerical radius”, J. Austral. Math. Soc. Ser. A 36 (1984), 130–133.CrossRefGoogle Scholar
[2]Bonsall, F.F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras (London Mathematical Society Lecture Note Series, 2. Cambridge University Press, Cambridge, 1971).CrossRefGoogle Scholar