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Interpolation and Spectra of Regular LP-Space Operators

Published online by Cambridge University Press:  20 November 2018

Karen Saxe
Karen Saxe*
Affiliation:
St. Olaf College, Northfield, MN, 55057 U. S. A.
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Abstract

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We consider the Banach algebra consisting of linear operators T which are defined on the simple functions and have bounded extensions Tp on LP for all values of p ∊ [1, ∞]. We show that the 'integral' operators in this algebra form a right ideal, and that each Tp associated to an integral T is regular. When the underlying measure is finite or special discrete we show further that every Tp is regular for every T in the algebra. Algebraic techniques together with interpolation results are then used to get relationships between the spectrum and the order spectrum of the associated Tp's.

Keywords

47A1047B55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 470 - 481
Copyright
Copyright © Canadian Mathematical Society 1990

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