Abstract
Ideals are the prime structural components of a vector lattice; accordingly, closed ideals are bound to play a decisive role in the theory of Banach lattices, and their study is the principal concern of this chapter. Its first part (Section 1–6) is concerned with the lattice of closed ideals of a Banach lattice, and with a representation theory for a wide class of Banach lattices (notably those containing quasi-interior positive elements) that ensues naturally. The second part of the chapter (Sections 7–11) then turns to various operator theoretic applications (mainly, mean ergodic theory), employing systematically the concept of operator-invariant ideal. A brief survey follows.
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© 1974 Springer-Verlag Berlin Heidelberg
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Schaefer, H.H. (1974). Ideal and Operator Theory. In: Banach Lattices and Positive Operators. Die Grundlehren der mathematischen Wissenschaften, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65970-6_3
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DOI: https://doi.org/10.1007/978-3-642-65970-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65972-0
Online ISBN: 978-3-642-65970-6
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