Analyticity of determinants of operators on a Banach space
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- by James S. Howland PDF
- Proc. Amer. Math. Soc. 28 (1971), 177-180 Request permission
Abstract:
If $F(z)$ is an analytic family of operators on a Banach space which is of finite rank for each $z$, then rank $F(z)$ is constant except for isolated points, and det $(I + F(z))$ and tr $F(z)$ are analytic. Similarly if $F(z)$ is meromorphic.References
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
- A. F. Ruston, On the Fredholm theory of integral equations for operators belonging to the trace class of a general Banach space, Proc. London Math. Soc. (2) 53 (1951), 109–124. MR 42612, DOI 10.1112/plms/s2-53.2.109
- A. F. Ruston, Auerbach’s theorem and tensor products of Banach spaces, Proc. Cambridge Philos. Soc. 58 (1962), 476–480. MR 165346, DOI 10.1017/s0305004100036744
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 177-180
- MSC: Primary 47A55; Secondary 47B10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0417827-4
- MathSciNet review: 0417827