Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-19T22:05:53.127Z Has data issue: false hasContentIssue false
  • English
  • Français

On eigenvalues and inverse singular values of compact linear operators in Hilbert space

Published online by Cambridge University Press:  24 October 2008

J. P. O. Silberstein  and
F. Smithies
J. P. O. Silberstein
Affiliation:
Box 4331 G.P.O., Melbourne C.1Australia
Get access Rights & Permissions [Opens in a new window]

Extract

1·1. In this paper we shall be concerned with the equations

where K is a compact (completely continuous) linear operator in a Hilbert space , K is the adjoint of K, I is the identity operator, x and y are elements of ∥ x ∥ denotes the norm of x, and κ and σ are complex numbers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 2 , April 1953 , pp. 201 - 212
Copyright
Copyright © Cambridge Philosophical Society 1953

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Chang, S. H.Trans. Amer. math. Soc. 67 (1949), 351–67.CrossRefGoogle Scholar
(2)Hellinger, E. and Toeplitz, O.Encyklopädie der mathematischen Wissenschaften, vol. 2, part 3, section 13 (Leipzig, 1927).Google Scholar
(3)Hille, E.Functional analysis and semi-groups (Colloq. Publ. Amer. math. Soc. no. 31, New York, 1948).Google Scholar
(4)Hille, E. and Tamarkin, J. D.Acta math., Stockh., 57 (1931), 1–76.CrossRefGoogle Scholar
(5)Nagy, B. v. Sz. Ergebn. Math. vol. 5, no. 5 (1942).Google Scholar
(6)Riesz, F.Les systèmes d'équations linéaires à une infinité d'inconnues (Collection Borel, Paris, 1913).Google Scholar
(7)Smithies, F.Proc. Lond. math. Soc. (2), 43 (1937), 255–79.Google Scholar
(8)Stone, M. H.Linear transformations in Hilbert space (Colloq. Publ. Amer. math. Soc. no. 15, New York, 1932).Google Scholar
(9)Weyl, H.Proc. nat. Acad. Sci., Wash., 35 (1949), 408–11.CrossRefGoogle Scholar
(10)Whittaker, E. T.Analytical dynamics, 4th ed. (Cambridge, 1937).Google Scholar