Abstract
Let L(λ) be an analytic matrix function, let F be a bounded and isolated part of its numerical range, and Γ be a closed contour of regular points of L(λ) with F inside Γ. Defining c(F) = indΓ (L(λ) f, f), f≠ 0, we give new proofs of the existence of spectral divisors of L(λ.) with respect toΓin the cases that either c(F) = 1 or Γ is a circle and, in both cases, there is no completeness hypothesis. Other results on the existence of Γ-spectral divisors (using completeness) are extended from the case of matrix polynomials to that of analytic matrix functions.
The authors were supported in part by grants from, respectively, the Natural Science and Engineering Research Council of Canada, and the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.
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© 2001 Springer Basel AG
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Lancaster, P., Markus, A. (2001). A Note on Factorization of Analytic Matrix Functions. In: Bart, H., Ran, A.C.M., Gohberg, I. (eds) Operator Theory and Analysis. Operator Theory: Advances and Applications, vol 122. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8283-5_12
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DOI: https://doi.org/10.1007/978-3-0348-8283-5_12
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