Abstract
This chapter concerns another important set of compact operators, namely the Hilbert-Schmidt operators. The class of Hilbert-Schmidt operators has a natural Hilbert space structure and it contains the trace class operators. In the first section some additional properties of s-numbers are derived. In the second section the Hilbert-Schmidt operators are introduced and their main properties are established. The last section contains a completeness theorem for eigenvectors and generalized eigenvectors of Hilbert-Schmidt operators.
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© 1990 Springer Basel AG
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Gohberg, I., Goldberg, S., Kaashoek, M.A. (1990). Hilbert-Schmidt Operators. In: Classes of Linear Operators Vol. I. Operator Theory: Advances and Applications, vol 49. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7509-7_9
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DOI: https://doi.org/10.1007/978-3-0348-7509-7_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7511-0
Online ISBN: 978-3-0348-7509-7
eBook Packages: Springer Book Archive