Abstract
The study of traces and determinants of trace class and Hilbert-Schmidt operators on Hilbert space requires a familiarity with these classes of operators. This chapter discusses all the related concepts and theorems needed in this book. Included are properties of singular numbers of compact operators and Lidskii’s trace theorem. We then proceed to introduce the regularized determinants of Hilbert-Schmidt operators. The formulas for the traces of integral operators with continuous kernel and with smooth kernel are presented. The determinant of operator pencils also appears. The last section treats the S p spaces which are generalizations of the algebra of Hilbert-Schmidt operators.
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© 2000 Springer Basel AG
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Gohberg, I., Goldberg, S., Krupnik, N. (2000). Trace Class and Hilbert-Schmidt Operators in Hilbert Space. In: Traces and Determinants of Linear Operators. Operator Theory Advances and Applications, vol 116. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8401-3_5
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DOI: https://doi.org/10.1007/978-3-0348-8401-3_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9551-4
Online ISBN: 978-3-0348-8401-3
eBook Packages: Springer Book Archive