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Symmetrisable operators*

Published online by Cambridge University Press:  09 April 2009

J. P. O. Silberstein
J. P. O. Silberstein
Affiliation:
University of Western Australia, Perth.
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About 14 years ago A. C. Zaanen [7] published a series of papers on compact symmetrisable linear operators in Hilbert space. Four years later I was encouraged by Dr. F. Smithies to study the spectral properties of general symmetrisable operators in Hilbert space and the resulting research formed the basis of part of a dissertation I submitted to the University of Cambridge in 1952 [4]. For various personal reasons I have not previously been able to, publish these results more widely, although I believe some of them, at least, to be of general interest.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 4 , December 1962 , pp. 381 - 402
Copyright
Copyright © Australian Mathematical Society 1962

References

[1]Dixmier, J., Bull. Soc. Mat. de France 77 (1949) 11–101.Google Scholar
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[3]Neumann v., J., Functional Operators II. Ann. of Math. Studies 22 Princeton 1950.Google Scholar
[4]Silberstein, J. P. O., On certain linear operators in Hilbert Space Dissertation, Cambridge03 1952.Google Scholar
[5]Silberstein, J. P. O., On the method of minimal iterations. Aeronautical Research Laboratories (Melbourne) Report SM201 (1952).Google Scholar
[6]Stone, , Linear, M. H. Transformations in Hilbert Space. A. M. S. Coll. Publ. XV New York 1932.Google Scholar
[7]Zaanen, A. C., Proc. Ak. v. Wetensch. Amsterdam 49 (1946) 194–204.Google Scholar
[8]Zaanen, A. C., Linear Analysis. Noordhoff, Groningen 1953.Google Scholar