Multiplicity theory and the outer boundary
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- by John S. Spraker PDF
- Proc. Amer. Math. Soc. 112 (1991), 391-392 Request permission
Abstract:
Let $f$ be a conformal map from the unit disk onto a simply-connected region $R$. Multiplication by $f$ on ${L^2}$ is a normal operator. In this paper it is shown that the outer boundary of $R$ is a set of multiplicity one for this operator.References
- M. B. Abrahamse, Multiplication operators, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977) Lecture Notes in Math., vol. 693, Springer, Berlin, 1978, pp. 17–36. MR 526530
- M. B. Abrahamse and Thomas L. Kriete, The spectral multiplicity of a multiplication operator, Indiana Univ. Math. J. 22 (1972/73), 845–857. MR 320797, DOI 10.1512/iumj.1973.22.22072
- Thomas L. Kriete III, An elementary approach to the multiplicity theory of multiplication operators, Rocky Mountain J. Math. 16 (1986), no. 1, 23–32. MR 829193, DOI 10.1216/RMJ-1986-16-1-23
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 391-392
- MSC: Primary 47B38; Secondary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1062837-2
- MathSciNet review: 1062837