Contractions et Hyperdistributions a Spectre de Carleson |
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Authors: | Kellay K. |
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Affiliation: | UFR de Mathématiques et Informatique, Université de Bordeaux 351 cours de la Libération, 33405 Talence Cedex, France. E-mail: kellay{at}math.u-bordeaux.fr |
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Abstract: | Let =(n)n1 be a log concave sequence such that lim infn+n/nc>0for some c>0 and ((log n)/n)n1 is nonincreasing for some<1/2. We show that, if T is a contraction on the Hilbertspace with spectrum a Carleson set, and if ||Tn||=O(n)as n tends to + with n11/(n log n)=+, then T is unitary. Onthe other hand, if n11/(n log n)<+, then there exists a (non-unitary)contraction T on the Hilbert space such that the spectrum ofT is a Carleson set, ||Tn||=O(n) as n tends to +, andlim supn+||Tn||=+. |
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