Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-20T18:57:09.422Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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[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