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

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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.

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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