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The universal multiplicity theory for analytic operator-valued functions

Published online by Cambridge University Press:  24 October 2008

Jón Arason  and
Robert Magnus
Jón Arason
Affiliation:
The University Science Institute, Dunhaga 3, 107 Reykjavik, Iceland
Robert Magnus
Affiliation:
The University Science Institute, Dunhaga 3, 107 Reykjavik, Iceland
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Extract

An analytic operator-valued function A is an analytic map A: D → L(E, E), where D = D(A) is an open subset of the complex plane C and E = E(A) is a complex Banach space. For such a function A the singular set σ(A) of A is defined as the set of points z ∈ D such that A(z) is not invertible. It is a relatively closed subset of D.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 315 - 320
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1[Arason, J. and Magnus, R.. An algebraic multiplicity theory for analytic operator-valued functions. Preprint RH-01–94, Science Institute, Reykjavik, 1994.Google Scholar
[2[Gohberg, I. C., Kaashoek, M. A. and Lay, D. C.. Equivalence, linearization, and decomposition of holomorphic operator functions. J. Funct. Anal. 28 (1978), 102–144.Google Scholar
[3[Magnus, R.. On the multiplicity of an analytic operator-valued function. Preprint RH-11–93, Science Institute, Reykjavik, 1993. To appear in Math. Scand.Google Scholar
[4[Kaashoek, M. A., Van Der Mee, C. V. M. and Rodman, L.. Analytic operator functions with compact spectrum. I. Spectral nodes, linearization and equivalence. Integral Equations Operator Theory 4 (1981), 504–547.CrossRefGoogle Scholar