The Douglas property for multiplier algebras of operators
  For a collection of reproducing kernels k which includes those for the Hardy space of the polydisk and ball and for the Bergman space, k is a complete Pick kernel if and only if the multiplier algebra of the Hilbert space H^2(k) associated to k has the Douglas property. Consequences for solving the operator equation AX=Y are examined. 
Scott McCullough and Tavan T. Trent
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