TY - JOUR
T1 - Weak-star generators of zn, n > 1, and transitive operator algebras
AU - Ansari, Mohamad A.
N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 1988/5
Y1 - 1988/5
N2 - 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.
AB - 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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U2 - 10.1090/S0002-9939-1988-0938656-1
DO - 10.1090/S0002-9939-1988-0938656-1
M3 - Article
AN - SCOPUS:84966207408
SN - 0002-9939
VL - 103
SP - 131
EP - 136
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 1
ER -