On Finite Elements in Lattices of Regular Operators |
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Authors: | Zi Li Chen Martin R Weber |
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Institution: | 1.Department of Mathematics,Southwest Jiaotong University Chengdu,Chengdu,P. R. China;2.Fachrichtung Mathematik,Technische Universit?t Dresden,Dresden,Germany |
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Abstract: | Let E and F be vector lattices and
the ordered space of all regular operators, which turns out to be a (Dedekind complete) vector lattice if F is Dedekind complete. We show that every lattice isomorphism from E onto F is a finite element in
, and that if E is an AL-space and F is a Dedekind complete AM-space with an order unit, then each regular operator is a finite element in
. We also investigate the finiteness of finite rank operators in Banach lattices. In particular, we give necessary and sufficient
conditions for rank one operators to be finite elements in the vector lattice
.
A half year stay at the Technical University of Dresden was supported by China Scholarship Council. |
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Keywords: | 46B42 47B07 47B65 |
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