Completely continuous Hankel operators on $H\sp \infty$ and Bourgain algebras
نویسندگان
چکیده
منابع مشابه
Hankel-Type Operators, Bourgain Algebras, and Uniform Algebras
Let H∞(D) denote the algebra of bounded analytic functions on the open unit disc in the complex plane. For a function g ∈ L∞(D), the Hankel-type operator Sg is defined by Sg(f) = gf +H∞(D). We give here an overview of the study of the symbol of the Hankel-type operator, with emphasis on those symbols for which the operator is compact, weakly compact, or completely continuous. We conclude with a...
متن کاملCompletely Continuous Banach Algebras
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...
متن کاملCompletely continuous Banach algebras
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 sufficient condition for an o...
متن کاملOn Completely Continuous Hankel Matrices1
1. Main theorem. Let x = (xo, xi, • • • ) be a sequence of complex numbers and let | x \ he the norm | x | = (^Z | x„ |2)1/2 2:0. Let an asterisk denote complex conjugation. If \x\ < <» and |y| < oo, let [x, y] = [y, x] denote the sum of the series ^T,xnyn, that is, the "scalar" product of y by x*. For a given x with a finite norm |x|, let x(t) denote a function of class i2(0, 27r) having the F...
متن کاملCompletely 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1989
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1989-0931727-6