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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An example in the theory of well-bounded operators


Authors: H. R. Dowson and P. G. Spain
Journal: Proc. Amer. Math. Soc. 32 (1972), 205-208
MSC: Primary 47.40
DOI: https://doi.org/10.1090/S0002-9939-1972-0288615-8
MathSciNet review: 0288615
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Abstract: If H is the Hilbert transform on $ {L^p}(Z)$, then $ T = \pi I + iH$ is a well-bounded operator for $ 1 < p < \infty $, but is not a scalar-type spectral operator except when $ p = 2$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0288615-8
Keywords: Well-bounded operators, scalar-type spectral operators, Hilbert transform
Article copyright: © Copyright 1972 American Mathematical Society