Vol. 24, No. 1, 1968

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Schwarz norms for operators

James Patrick Williams

Vol. 24 (1968), No. 1, 181–188
Abstract

Let H be a complex Hilbert space and let (H) be the algebra of bounded linear operators from H into itself. A norm | | on (H) which is equivalent to the usual norm will be called a Schwarz norm if the following version of the Schwarz lemma is valid for | |:

SCHWARZ LEMMA If f is analytic and bounded by 1 in |z| < 1, and if f(0) = 0, then |f(T) |T| for each operator T with |T| < 1.

Mathematical Subject Classification
Primary: 46.50
Milestones
Received: 17 March 1967
Published: 1 January 1968
Authors
James Patrick Williams