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A note on the joint operator norm of hermitian operators on Banach spaces

Published online by Cambridge University Press:  18 May 2009

Muneo Chō  and
Tadasi Huruya
Muneo Chō
Affiliation:
Department of Mathematics, Joetsu University of Education, Joetsu 943, Japan
Tadasi Huruya
Affiliation:
Faculty of Education, Niigata University, Niigata 950-21, Japan
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Let X be a complex Banach space and H be a hermitian operator on X. Then in [7] Sinclair proved that r(H) = ¶H¶, where r(H) and ¶H¶ are the spectral radius and the operator norm of H, respectively.

For a commuting n-tuple T = (T1,…, Tn) of operators on X, we denote the (Taylor) joint spectrum of T by σ(T) (see [9]) and define the joint operator norm ¶T¶ and the joint spectral radius r(T) by

and

respectively.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 219 - 220
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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