Abstract
In this chapter we further specify Theorem 2.2.2 for compact Hilbert space operators of order one. Such operators are Hilbert-Schmidt operators and not necessarily trace class operators. We begin with some remarks about the latter class of operators. Throughout this chapter we shall use terminology and basic facts from the theory of entire functions which can be found in Chap. 14.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A.D. Baranov, D.V. Yakubovich, One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum. J. Math. Anal. Appl. 424, 1404–1424 (2015)
I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators (American Mathematical Society, Providence, 1969)
I. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of Linear Operators I (Birkhäuser Verlag, Basel, 1990)
A.P. Khromov, Finite-dimensional perturbations of Volterra operators. J. Math. Sci. 138, 5593–6066 (2006)
C. Liaw, S. Treil, Rank one perturbations and singular integral operators. J. Funct. Anal. 257, 1947–1975 (2009)
A.A. Shkalikov, Perturbations of self-adjoint and normal operators with discrete spectrum. Russ. Math. Surv. 71, 907–964 (2016)
S.M. Verduyn Lunel, D.V. Yakubovich, A functional model approach to linear neutral functional differential equations. Integr. Equ. Oper. Theory 27, 347–378 (1997)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kaashoek, M.A., Verduyn Lunel, S.M. (2022). Compact Hilbert Space Operators of Order One. In: Completeness Theorems and Characteristic Matrix Functions. Operator Theory: Advances and Applications, vol 288. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-04508-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-031-04508-0_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-04507-3
Online ISBN: 978-3-031-04508-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)