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On some classes of weighted composition operators

Published online by Cambridge University Press:  18 May 2009

James T. Campbell  and
James E. Jamison
James T. Campbell
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, Tennessee 38152, USA
James E. Jamison
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, Tennessee 38152, USA
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Let (X, Σμ) denote a complete a-finite measure space and T: X → X a measurable (T-1A ε Σ each A ε Σ) point transformation from X into itself with the property that the measure μ°T-1 is absolutely continuous with respect to μ. Given any measurable, complex-valued function w(x) on X, and a function f in L2(μ), define WTf(x) via the equation

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 1 , January 1990 , pp. 87 - 94
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Bastian, J. J., A decomposition of weighted translation operators, Trans. Amer. Math. Soc. 224 (1976), 217–230.Google Scholar
2.Campbell, J. T. and Dibrell, P., Hyponormal powers of composition operators, Proc. Amer. Math. Soc. 102 (1988), 914–918.Google Scholar
3.Harrington, D. J. and Whitley, R., Seminormal composition operators, J. Operator Theory 11 (1984), 125–135.Google Scholar
4.Lambert, A., Hyponormal composition operators, Bull. Lond. Math. Soc. 18 (1986), 395–400.CrossRefGoogle Scholar
5.Lambert, A., Personal communication, 1987.Google Scholar
6.Whitley, R., Normal and quasinormal composition operators, Proc. Amer. Math. Soc. 70 (1978), 114–118.CrossRefGoogle Scholar