The commutant of a certain compression

Author:
William T. Ross

Journal:
Proc. Amer. Math. Soc. **118** (1993), 831-837

MSC:
Primary 47B38; Secondary 47A20, 47B35

DOI:
https://doi.org/10.1090/S0002-9939-1993-1145951-4

MathSciNet review:
1145951

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be any bounded region in the complex plane and be a simple compact arc of class . Let (resp. ) be the Bergman space on (resp. ). Let be the operator multiplication by on and be the compression of to the semi-invariant subspace . We show that the commutant of is the set of all operators of the form , where is a multiplier on a certain Sobolev space of functions on and . We also use multiplier theory in fractional order Sobolev spaces to obtain further information about .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1145951-4

Keywords:
Bergman spaces,
multiplication operators,
Sobolev spaces,
multipliers

Article copyright:
© Copyright 1993
American Mathematical Society