Weak-star generators of zn, n > 1, and transitive operator algebras

Research output: Contribution to journalArticle

Abstract

A function/ in H∞ is said to be a weak-star generator (w*-gen.) of the function en(z) = zn, \z\ < 1, n=, 1 if lim∝ p ° f = en (w*-topology), for some net (p of complex polynomials. For the case n = 1, f is called a w*- gen. of H The w*-generators of H have been defined and characterized by Sarason. It is the purpose of the present paper to give necessary and sufficient conditions for a function to generate en. As a result, it follows from our characterization that certain analytic Toeplitz operators have the transitive algebra property.

Original languageEnglish (US)
Pages (from-to)131-136
Number of pages6
JournalProceedings of the American Mathematical Society
Volume103
Issue number1
DOIs
StatePublished - Jan 1 1988

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Operator Algebras
Algebra
Stars
Mathematical operators
Star
Generator
Complex Polynomials
Toeplitz Operator
Topology
Polynomials
Necessary Conditions
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "A function/ in H∞ is said to be a weak-star generator (w*-gen.) of the function en(z) = zn, \z\ < 1, n=, 1 if lim∝ p∝ ° f = en (w*-topology), for some net (p∝ of complex polynomials. For the case n = 1, f is called a w*- gen. of H∞ The w*-generators of H∞ have been defined and characterized by Sarason. It is the purpose of the present paper to give necessary and sufficient conditions for a function to generate en. As a result, it follows from our characterization that certain analytic Toeplitz operators have the transitive algebra property.",
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Weak-star generators of zn, n > 1, and transitive operator algebras. / Ansari, Mohamad A.

In: Proceedings of the American Mathematical Society, Vol. 103, No. 1, 01.01.1988, p. 131-136.

Research output: Contribution to journalArticle

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