A Class of Sub-Hardy Hilbert Spaces Associated with Weighted Shifts
  In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted shifts. The well known results of de Branges and Beurling are deduced as corollaries . 
Sneh Lata, Dinesh Singh
math.FA