✦ LIBER ✦
Simplicial cones and the existence of shape-preserving cyclic operators
✍ Scribed by B.L. Chalmers; M.P. Prophet; J.M. Ribando
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 232 KB
- Volume
- 375
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
Let X denote a real Banach space, X * its dual space and V an n-dimensional subspace of X. Given a weak * -closed cone S * ⊂ X * , we say that f ∈ X has shape if f, φ 0 for all φ ∈ S * . Let S ⊂ X denote the cone of elements having shape. Suppose the linear operator P : V → V leaves S invariant (i.e., P (S ∩ V ) ⊂ S). We seek extensions P of P to X that leave S invariant; i.e. P : X → V such that P | V = P and P S ⊂ S. We say that such an extension is shape-preserving. It is shown in Chalmers and Prophet [