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The integral formula for the reduced algebraic multiplicity of meromorphic operator functions

Published online by Cambridge University Press:  20 January 2009

H. Bart ,
M. A. Kaashoek  and
D. C. Lay
H. Bart
Affiliation:
Wiskundig Seminarium, Vrije University, Amsterdam-11
M. A. Kaashoek
Affiliation:
Wiskundig Seminarium, Vrije University, Amsterdam-11
D. C. Lay
Affiliation:
Department of Mathematics, University of Maryland, College Park, Md. 20742
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Throughout this paper A denotes an operator function, holomorphic on a deletedneighborhood of a complex number λo, with values in the space ℒ(X,Y) of boundedlinear operators between two complex Banach spaces X and Y. In his survey article(7), I. C. Gohberg has defined for such an arbitrary operator function A the algebraic multiplicity RM(A;λo) and the reduced algebraic multiplicity RM(A;λo) of A at λo. In earlier papers (e.g., (8, 16)) these notions have been defined and studied for morerestricted classes of operator functions. In (8) Gohberg and Sigal treated the case when A is finite-meromorphic at λo, A(λ) is bijective for λ in some deleted neighbor-hood of λo and the constant term A0 in the Laurent expansion of A at λo is aFredholm operator. They proved that in this case

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 1 , March 1978 , pp. 65 - 71
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

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