Cyclic elements in some spaces of analytic functions

  title={Cyclic elements in some spaces of analytic functions},
  author={Boris Korenblum},
  journal={Bulletin of the American Mathematical Society},
  • B. Korenblum
  • Published 1 November 1981
  • Mathematics, Philosophy
  • Bulletin of the American Mathematical Society
DEFINITIONS. 1. A~ (p > 0) is the Banach space of analytic functions f(z) in U = {z G C| \z\ < 1} that satisfy \f(z)\ = o[(l \z\)~] (\z\ > 1) with the norm \\f\\ = max{ |f(z)\(l z)} (z G If). Note that fn —• ƒ in A * and #„ —># m A~~' impl ies /^ —>,/& in A~\ 2. B (p> 0) is the Bergman space, i.e., the "analytic" subspace of L(rdrd6) in U. 3. A -00 = U A~ = U B (p > 0). A~°° is a linear topological space [1]. 4. Pis the set of all algebraic polynomials P(z). Pis dense in any of the spaces A _ p… 
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