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The Toeplitz-Hausdorff Theorem Explained

Published online by Cambridge University Press:  20 November 2018

Chandler Davis
Chandler Davis*
Affiliation:
University of Toronto, Toronto, Ontario
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Paul Halmos expressed [3, p. 110] the general dissatisfaction with the usual proofs of this famous and important theorem. They all make it seem like an accidental product of a computation. A more conceptual proof was devised by N. P. Dekker. In spite of the elegance of his proof, the one offered below may have some claim to be regarded as "the reason the theorem is true".

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 245 - 246
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Davis, Ch., The shell of a Hilbert-space operator—II. Acta Sci. Math, (to appear).Google Scholar
2. Dekker, N. P., Joint numerical range and joint spectrum of Hilbert space operators, Amsterdam thesis, 1969.Google Scholar
3. Halmos, P. R., A Hilbert space problem book, Van Nostrand, Princeton, N.J., 1967.Google Scholar