Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T07:25:40.296Z Has data issue: false hasContentIssue false
  • English
  • Français

Finitely spectral operators

Published online by Cambridge University Press:  18 May 2009

B. Nagy
B. Nagy
Affiliation:
University of Technology, Budapest, Hungary
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 the theory of spectral (and prespectral) operators in a Banach space or in a locally convex topological vector space the countable additivity (in some topology) of a resolution of the identity of the operator is a standing assumption. One might wonder why. Even if one cannot completely agree with the opinion of Diestel and Uhl ([6, p. 32]) stating that “countable additivity [of a set function] is often more of a hindrance than a help”, it might be interesting to study which portions of the theory of (pre)spectral operators and in which form extend to the more general situation described below.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 1 , January 1986 , pp. 95 - 112
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

1.Albrecht, E., On some classes of generalized spectral operators, Arch Math. (Basel), 30 (1978), 297–303.CrossRefGoogle Scholar
2.Albrecht, E., On decomposable operators, Integral Equations and Operator Theory, 2 (1979), 1–10.CrossRefGoogle Scholar
3.Bade, W. G. and Curtis, P. C. Jr, Homomorphisms of commutative Banach algebras, Amer. J. Math., 82 (1960), 589–608.CrossRefGoogle Scholar
4.Berkson, E. and Dowson, H. R., Prespectral operators, Illinois J. Math., 13 (1969), 291–315.CrossRefGoogle Scholar
5.Colojoara, I. and Foias, C., Theory of generalized spectral operators (Gordon and Breach, New York, 1968).Google Scholar
6.Diestel, J. and Uhl, J. J. Jr, Vector measures. Math. Surveys, No. 15 (Amer. Math. Soc., Providence, 1977).CrossRefGoogle Scholar
7.Dowson, H. R., Spectral theory of linear operators (Academic Press, London, 1978).Google Scholar
8.Dunford, N., A survey of the theory of spectral operators, Bull. Amer. Math. Soc., 64 (1958), 217–274.CrossRefGoogle Scholar
9.Dunford, N. and Schwartz, J. T., Linear operators, Part I: General theory (Wiley, New York, 1958).Google Scholar
10.Edwards, R. E., Functional analysis (Holt, Rinehart and Winston, New York, 1965).Google Scholar
11.Fixman, U., Problems in spectral operators, Pacific J. Math., 9 (1959), 1029–1051.CrossRefGoogle Scholar
12.Floret, K. and Wloka, J., Einführung in die Theorie der lokalkonvexen Räume (Springer-Verlag, Berlin, 1968).CrossRefGoogle Scholar
13.Gillespie, T. A., Spectral measures on spaces not containing l ∞, Proc. Edinburgh Math. Soc. (2), 24 (1981), 41–45.CrossRefGoogle Scholar
14.Gillespie, T. A., Bade functional, Proc. Roy. Irish Acad. Sect. A, 81 (1981), 13–23.Google Scholar
15.Kelley, J. and Namioka, I., Linear topological spaces (Van Nostrand, New York, 1963).CrossRefGoogle Scholar
16.Köthe, G., Topological vector spaces I (Springer-Verlag, Berlin, 1969).Google Scholar
17.Lange, R., On generalization of decomposability, Glasgow Math. J., 22 (1981), 77–81.CrossRefGoogle Scholar
18.Lewis, D. R., Integration with respect to vector measures, Pacific J. Math., 33 (1970), 157–165.CrossRefGoogle Scholar
19.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I (Springer-Verlag, Berlin, 1977).CrossRefGoogle Scholar
20.Nagy, B., Operators with the spectral decomposition property are decomposable, Studia Sci. Math. Hungar., 13 (1978), 429–432.Google Scholar
21.Nagy, B., On Boolean algebras of projections and prespectral operators, pp. 145–162 in: Invariant subspaces and other topics. Operator theory Vol. 6 (Birkhäuser, Basel, 1982).CrossRefGoogle Scholar
22.Schaefer, H. H., Convex conves and spectral theory, pp. 451–471 in: Proc. Sympos. Pure Math., Vol. VII (Amer. Math. Soc. Providence, 1963).Google Scholar
23.Sikorski, R., Boolean algebras (Springer-Verlag, Berlin, 1964).Google Scholar
24.Spain, P. G., On scalar-type spectral operators, Proc. Cambridge Philos. Soc., 69 (1971), 409–410.CrossRefGoogle Scholar
25.Vasilescu, F.-H., Analytic functional calculus and spectral decompositions (Reidel, 1982).Google Scholar