Abstract
Let X and Y be complex B-spaces, and let S be the unit sphere in X. An operator T ∈ L (X, Y) is said to be compact or completely continuous if the image T · S is relatively compact in Y. For a compact operator T ∈ L(X, X), the eigenvalue problem can be treated fairly completely, in the sense that the classical theory of Fredholm concerning linear integral equations may be extended to the linear functional equation Tx - λx = ywith a complex parameter λ. This result is known as the Riesz-Schauder theory. F. Riesz [2] and J. Schauder [1].
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© 1974 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1974). Compact Operators. In: Functional Analysis. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96208-0_11
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DOI: https://doi.org/10.1007/978-3-642-96208-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-96210-3
Online ISBN: 978-3-642-96208-0
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