Vol. 26, No. 1, 1968

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Strong continuity of operator functions

Richard Vincent Kadison

Vol. 26 (1968), No. 1, 121–129

The complex-valued functions defined on a subset S of the plane such that (SS)S is empty which give strong-operator continuous mappings from the set of normal operators on a Hilbert space with spectra in S into the set of all normal operators are characterized as those which are continuous on S, bounded on bounded subsets of S and O(z) (Theorem 4.2). In the process of proving this result, it is shown that the adjoint operation is strong-operator continuous on the set of normal operators (Theorem 4.1).

Mathematical Subject Classification
Primary: 46.65
Received: 26 May 1967
Published: 1 July 1968
Richard Vincent Kadison
Mathematics Department
University of Pennsylvania
209 South 33rd Street
Philadelphia PA 19104-6395
United States