In this section we will treat special classes of regular operators. First we will consider disjointness preserving operators which are closely related to lattice homomorphisms. We will show that every continuous disjointness preserving operator T is regular and has an absolute value such that |Tx| = |Tx| for all x ∈E + . Furthermore, we will introduce the center Z(E) of E. We will apply this concept to deduce an approximation theorem for operators in the spirit of Freudenthal’s spectral theorem.
Weitere Kapitel dieses Buchs durch Wischen aufrufen
- Operators on Riesz Spaces and Banach Lattices
- Springer Berlin Heidelberg
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