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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Conditions for restricted translation operators to belong to $ S\sb{p}$


Authors: Harry Dym and Isidor Shapiro
Journal: Proc. Amer. Math. Soc. 63 (1977), 251-258
MSC: Primary 47B37; Secondary 30A78
MathSciNet review: 0448143
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Abstract: Let B be a Blaschke product, let P be the orthogonal projection of $ {L^2}({R^1})$ onto the left invariant subspace $ {H^2} \ominus B{H^2}$ and let $ {E_t}:f(\gamma ) \to {e^{ - i\gamma t}}f(\gamma )$. Conditions are given on the roots of B for $ P{E_t}P$ to belong to $ {S_p}, 0 < p < \infty$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0448143-8
PII: S 0002-9939(1977)0448143-8
Keywords: Compact operators, trace class, Hilbert Schmidt class, $ {S_p}$ class, translation invariant subspaces, semigroups
Article copyright: © Copyright 1977 American Mathematical Society



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