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Symmetrisable operators :Part III Hilbert space operators Symmetrisable by bounded operators

Published online by Cambridge University Press:  09 April 2009

J. P. O. Silberstein
J. P. O. Silberstein
Affiliation:
Department of Mathematics, University of Western Australia.
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The fact that the most general symmetrisable operators in Hilbert Space do not possess a number of the desirable properties of such operators in unitary spaces makes it necessary to look for a more restricted class of operators. There are two reasons for our particular choice. In the first place many of the conditions introduced in the course of Part II concerned reltionships between the domain of the symmetrising operator H and the domain and range of the symmetrisable operator A. These conditions are now all automatically satisfied. The other reason is that the construction used in section 4 to relate symmetrisable operators to certain symmetric operators clearly required that either H or H−1 was bounded. The case of H−1 bounded has already been dealt with in section 9 and shown to be fairly simple. The case in which H is bounded is clearly of considerable complexity, since we have already seen (example in proof of Theorem 10.6.) that the con |H| the bound of H by

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1964 , pp. 31 - 48
Copyright
Copyright © Australian Mathematical Society 1964

References

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