Completely continuous composition operators
نویسندگان
چکیده
منابع مشابه
Completely Continuous Composition Operators
A composition operator Tbf = f o b is completely continuous on H1 if and only if \b\ < 1 a.e. If the adjoint operator Tg is completely continuous on VMOA , then 7¿ is completely continuous on Hl . Examples are given to show that the converse fails in general. Two results are given concerning the relationship between the complete continuity of an operator and of its adjoint in the presence of ce...
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We consider the completely positive map on the Toeplitz operator system given by conjugation by a composition operator; that is, we analyze operators of the form C∗ φTfCφ We prove that every such operator is weakly asymptotically Toeplitz, and compute its asymptotic symbol in terms of the Aleksandrov-Clark measures for φ. When φ is an inner function, this operator is Toeplitz, and we show under...
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For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a suffici...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1994
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1994-1257642-5