Titlebook: Banach Lattices; Peter Meyer-Nieberg Textbook 1991 Springer-Verlag Berlin Heidelberg 1991 Banach lattices.Banachscher Verband.Positive Ope

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Banach Lattices978-3-642-76724-1Series ISSN 0172-5939 Series E-ISSN 2191-6675

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0172-5939 Overview: 978-3-540-54201-8978-3-642-76724-1Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Zelluloseester- und Zelluloseätherfasernry of Riesz spaces. An important result presented here is Kakutani’s representation theorem for an M-spaces with a unit. It plays still an important role in the theory of Riesz spaces, although many proofs which were originally based on this representation theorem now can be replaced by shorter and simpler lattice theoretical arguments.

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Operators on Riesz Spaces and Banach Lattices, to lattice homomorphisms. We will show that every continuous disjointness preserving operator . is regular and has an absolute value such that |.| = |.| for all . ∈... Furthermore, we will introduce the center . of .. We will apply this concept to deduce an approximation theorem for operators in the spirit of Freudenthal’s spectral theorem.

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Spectral Theory of Positive Operators,pectral behaviour of positive linear operators including the Krein-Rutman theorems. We will formulate and prove these theorems only for Banach lattices, although they hold with similar proofs for more general classes of ordered Banach spaces. The interested reader will find these general versions in Schaefer (1971), appendix.

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https://doi.org/10.1007/978-3-642-60425-6In this section we mainly are interested in showing characterizations of properties of subspaces of Banach lattices. Moreover we will use the theory of order weakly compact operators to prove some results for arbitrary Banach spaces. First we will recall some basic facts concerning Schauder bases and topological embeddings of ...