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. © 2018 University of Houston. All rights reserved.

Sneh Lata

Mathematics

(SoNS) School of Natural Sciences

Singh D.

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