Multiplicity theory and the outer boundary

Author:
John S. Spraker

Journal:
Proc. Amer. Math. Soc. **112** (1991), 391-392

MSC:
Primary 47B38; Secondary 47B15

MathSciNet review:
1062837

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Abstract: Let be a conformal map from the unit disk onto a simply-connected region . Multiplication by on is a normal operator. In this paper it is shown that the outer boundary of is a set of multiplicity one for this operator.

**[1]**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****[2]**M. B. Abrahamse and Thomas L. Kriete,*The spectral multiplicity of a multiplication operator*, Indiana Univ. Math. J.**22**(1972/73), 845–857. MR**0320797****[3]**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**, 10.1216/RMJ-1986-16-1-23

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1062837-2

Keywords:
Multiplicity,
multiplication operator

Article copyright:
© Copyright 1991
American Mathematical Society