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Interpolation and inequalities for functions of exponential type: the Arens irregularity of an extremal algebra

Published online by Cambridge University Press:  18 May 2009

M. J. Crabb  and
C. M. McGregor
M. J. Crabb
Affiliation:
Department Of MathematicsUniversity Of GlasgowGlasgow G12 8QW
C. M. McGregor
Affiliation:
Department Of MathematicsUniversity Of GlasgowGlasgow G12 8QW
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For any compact convex set K ⊂ ℂ there is a unital Banach algebra Ea(K) generated by an element h in which every polynomial in h attains its maximum norm over all Banach algebras subject to the numerical range V(h) being contained in K, [1]. In the case of K a line segment in ℝ, we show here that Ea(K) does not have Arens regular multiplication. We also show that ideas about Ea(K) give simple proofs of, and extend, two inequalities of C. Frappier [4].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 325 - 326
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

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