Abstract
Compact operators are often more easily studied than arbitrary bounded operators. In this chapter we show that compact (in fact, polynomially compact) operators have non-trivial invariant subspaces; much more general results are obtained in Chapter 8. We also show that the properties of normality and quasinilpotence for compact operators are determined by their invariant subspaces, and give examples of attainable lattices that are not attainable by compact operators.
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© 1973 Springer-Verlag Berlin Heidelberg
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Radjavi, H., Rosenthal, P. (1973). Compact Operators. In: Invariant Subspaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65574-6_6
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DOI: https://doi.org/10.1007/978-3-642-65574-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65576-0
Online ISBN: 978-3-642-65574-6
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