Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T05:05:16.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Biquasitriangularity and spectral continuity

Published online by Cambridge University Press:  18 May 2009

Ridgley Lange
Ridgley Lange
Affiliation:
Central Michigan University, Mount Pleasant, Michigan 48859
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 [6] Conway and Morrell characterized those operators on Hilbert space that are points of continuity of the spectrum. They also gave necessary and sufficient conditions that a biquasitriangular operator be a point of spectral continuity. Our point of view in this note is slightly different. Given a point T of spectral continuity, we ask what can then be inferred. Several of our results deal with invariant subspaces. We also give some conditions characterizing a biquasitriangular point of spectral continuity (Theorem 3). One of these is that the operator and its adjoint both have the single-valued extension property.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 2 , July 1985 , pp. 177 - 180
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCE

1.Albrecht, E., An example of a weakly decomposable operator that is not decomposable, Rev. Roum. Math Pures Appl. 20 (1975), 555–561.Google Scholar
2.Apostol, C., Quasitriangularity in Hilbert space, Indiana Univ. Math. J. 22 (1972/1973), 817–825.CrossRefGoogle Scholar
3.Apostol, C., Foias, C. and Voiculescu, D., Some results on non-quasitriangular operators. IV, Rev. Roum. Math. Pures Appl. 18 (1973), 487–514.Google Scholar
4.Berger, C. A. and Shaw, B. I., Intertwining, analytic structure, and the trace norm estimate, Lecture Notes in Mathematics No. 345 (Springer-Verlag, 1973).Google Scholar
5.Brown, L., Douglas, R. G. and Fillmore, P., Unitary equivalence modulo the compact operators and extensions of C*-algebras, Lecture Notes in Mathematics No. 345 (Springer-Verlag, 1973).Google Scholar
6.Conway, J. B. and Morrell, B., Operators that are points of spectral continuity, Integral Equations and Operator Theory, 2 (1979), 174–198.CrossRefGoogle Scholar
7.Dunford, N. and Schwartz, J. T., Linear operators Part III (Wiley, 1971).Google Scholar
8.Finch, J., The single valued extension property in a Banach space, Pacific J. Math. 58 (1975), 61–69.CrossRefGoogle Scholar
9.Frunza, S., A duality theorem for decomposable operators. Rev. Roum. Math. Pures Appl. 16 (1971), 1055–1058.Google Scholar
10.Herrero, D., Possible structure for the set of cyclic vectors, Indiana Univ. Math. J. 28 (1978), 913–926.CrossRefGoogle Scholar
11.Jafarian, A., Weak and quasidecomposable operators, Rev. Roum. Math. Pures Appl. 22 (1977), 195–212.Google Scholar
12.Lange, R., Duality and asymptotic spectral decomposition, preprint.Google Scholar