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A formula for the resolvent of a Reynolds operator

Published online by Cambridge University Press:  09 April 2009

J. B. Miller
J. B. Miller
Affiliation:
Monash University Melbourne
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Let be a complex Banach algebra, possibly non-commutative, with identity e. By a Reynolds operator we mean here a bounded linear operator T: → satisfying the Reynolds identity for all x, y ∈ . We prove that under certain conditions the resolvent of T, R(p, T) = (pI−T)−1, has the form where s = −log(e−Te) and exp y = e+y+y2/2!+….

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 3 , August 1968 , pp. 447 - 456
Copyright
Copyright © Australian Mathematical Society 1968

References

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