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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics