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On well-bounded operators of class Г

Published online by Cambridge University Press:  18 May 2009

Adnan A. S. Jibril
Adnan A. S. Jibril
Affiliation:
Yarmouk University, Irbid-Jordan
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Let T be a linear operator acting in a Banach space X. It has been shown by Smart [5] and Ringrose [3] that, if X is reflexive, then T is well-bounded if and only if it may be expressed in the form

where {E(λ)} is a suitable family of projections in X and the integral exists as the strong limit of Riemann sums.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 1 , January 1983 , pp. 1 - 5
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

REFERENCES

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5.Smart, D. R., Conditionally convergent spectral expansions. J. Austral. Math. Soc. 1 (1960) 319–333.Google Scholar
6.Turner, J. K., On well-bounded and decomposable operators. Proc. London Math. Soc. (3) 37 (1978), 521–544.Google Scholar