Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-20T00:49:46.837Z Has data issue: false hasContentIssue false
  • English
  • Français

Bishop's Condition (β)†

Published online by Cambridge University Press:  18 May 2009

Jon C. Snader
Jon C. Snader
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 1959, Bishop [4] published a seminal paper in which he studied various types of spectral decompositions or “duality theories” that an arbitrary bounded linear operator on a reflexive Banach space might have. In the course of his investigations, he isolated the following analytic property which he called condition (β).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 35 - 46
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Albrecht, E., On decomposable operators, Integral Equations and Operator Theory 2 (1977), 1–10.CrossRefGoogle Scholar
2.Apostol, C., Restrictions and quotients of decomposable operators in a Banach space, Rev. Roumaine Math. Pares Appl. 13 (1968), 147–150.Google Scholar
3.Apostol, C. and Bartle, R. G., The sum and product of decomposable operators, preprint.Google Scholar
4.Bishop, E., A duality theorem for arbitrary operators, Pacific J. Math. 9 (1959), 379–397.CrossRefGoogle Scholar
5.Colojoara, I. and Foias, C., Theory of generalized spectral operators, (Gordon and Breach, New York, 1968).Google Scholar
6.Dowson, H. R., Spectral theory of linear operators, (Academic Press, 1978).Google Scholar
7.Dunford, N., Spectral operators, Pacific J. Math. 4 (1954), 321–354.CrossRefGoogle Scholar
8.Dunford, N. and Schwartz, J. T., Linear operators, (Wiley-Interscience, 1958).Google Scholar
9.Erdelyi, I. and Lange, R., Operators with spectral decomposition properties, J. Math. Anal. Appl. 66 (1978), 1–19.CrossRefGoogle Scholar
10.Finch, J. K., The single-valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61–69.CrossRefGoogle Scholar
11.Foiaş, C., On the maximal spectral spaces of a decomposable operator, Rev. Roumaine Math. Pures Appl. 15 (1970), 1599–1606.Google Scholar
12.Frunzǎ, S., A complement to the duality theorem for decomposable operators, preprint.Google Scholar
13.Frunzǎ, S., Spectral decomposition and duality, Illinois J. Math. 20 (1976), 314–321.CrossRefGoogle Scholar
14.Halmos, P. R., A Hilbert space problem book, (Van Nostrand, 1967).Google Scholar
15.Herrero, D., Indecomposable compact perturbations of the bilateral shift, Proc. Amer. Math. Soc. 62 (1977), 254–258.CrossRefGoogle Scholar
16.Lange, R., A purely analytic criterion for a decomposable operator, Glasgow Math. J. 21 (1980), 69–70.CrossRefGoogle Scholar
17.Lange, R., On generalization of decomposability, Glasgow Math. J. 22 (1981), 77–81.CrossRefGoogle Scholar
18.Lange, R., Strongly analytic subspaces, in Operator theory and functional analysis, edited by Erdelyi, I., Research Notes in Mathematics #38, (Pitman, San Francisco, 1979).Google Scholar
19.Nagy, B., Operators with the spectral decomposition property are decomposable, preprint.Google Scholar
20.Radjabalipour, M., Equivalence of decomposable and 2-decomposable operators, Pacific J. Math. 77 (1978), 243–247.CrossRefGoogle Scholar
21.Snader, J. C., On T-strongly decomposable operators, to appear.Google Scholar
22.Snader, J. C., Strongly analytic subspaces and strongly decomposable operators, Pacific J. Math., to appear.Google Scholar
23.Vasilescu, F.-H., On asymptotic behavior of operators, Rev. Roumaine Math. Pures Appl. 12 (1967), 353–358.Google Scholar