The Metric Fuglede Property and Normality

Moore, R. L. ; Weiss, G.

Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 516-525

Résumé

In [4], H. Kamowitz considered the condition, to be satisfied by a bounded operator N on a Hilbert space , that for all operators X on . Kamowitz discovered that such an N must be normal and its spectrum must lie on a line or a circle; that is, N must be of the form αJ + β, where α and β are complex numbers and J is either Hermitian or unitary. G. Weiss [5] showed that the Hilbert-Schmidt norm behaves differently: N need only be normal in order that for all finite-rank operators X, and in fact this condition is equivalent to normality. Actually, the result in [5] removes the restriction that X be finite-rank, that is, if N is normal and X is any bounded operator, then

Détail

DOI : 10.4153/CJM-1983-029-9

Bibliographie

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