| Autor: |
Y.A. Abramovich, A. K. Kitover |
| Rok vydání: |
2002 |
| Předmět: |
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| Zdroj: |
Indagationes Mathematicae. 13(2):143-167 |
| ISSN: |
0019-3577 |
| DOI: |
10.1016/s0019-3577(02)80001-5 |
| Popis: |
The following four main results are proved here. Theorem 3.3. For each one-to-one band preserving operator T:X → X on a vector lattice its inverse T−1:T(X) → X is also band preserving. This answers a long standing open question. The situation is quite different if we move from endomorphisms to more general operators. Theorem 4.2. For a vector lattice X the following two conditions are equivalent: 1. i)|For each one-to-one band preserving operator T:X → Xu from X to its universal completion Xu the inverse T−1 is also band preserving. 2. ii)|For each non-zero x ϵ X and each non-zero band U ⊂ {x}dd there exists a non-zero semi-component of x in U. Theorem 5.1. For a vector lattice X the following two conditions are equivalent. 1. i)|Each band preserving operator T:X → Xu is regular. 2. ii)|The d-dimension of X equals 1. Corollary 5.9. Let X be a vector sublattice of C(K) separating points and containing the constants, where K is a compact Hausdorff space satisfying any one of the following three conditions: K is metrizable, or connected, or locally connected. Then each band preserving operator T: X → X is regular. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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