Davis-Wielandt shells of normal operators
For a finite-dimensional operator A with spectrum cr(A), the following conditions on the Davis-Wielandt shell DW(A) of A are equivalent: (a) A is normal. (b) DW(A) is the convex hull of the set {(A, |A|2 ) : A e cr(A)}. (c) DW(A) is a polyhedron. These conditions are no longer equivalent for an infi...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
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| Sorozat: | Acta scientiarum mathematicarum
75 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16302 |
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| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Li Chi-Kwong | |
| 245 | 1 | 0 | |a Davis-Wielandt shells of normal operators |h [elektronikus dokumentum] / |c Li Chi-Kwong |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2009 | ||
| 300 | |a 289-297 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 75 No. 1-2 | |
| 520 | 3 | |a For a finite-dimensional operator A with spectrum cr(A), the following conditions on the Davis-Wielandt shell DW(A) of A are equivalent: (a) A is normal. (b) DW(A) is the convex hull of the set {(A, |A|2 ) : A e cr(A)}. (c) DW(A) is a polyhedron. These conditions are no longer equivalent for an infinite-dimensional operator A. In this note, a thorough analysis is given for the implication relations among these conditions. From the main result, one can deduce the equivalent conditions (a)-(c) for a finite-dimensional operator A, and show that the DavisWielandt shell cannot be used to detect normality for infinite-dimensional operators. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Matematika | ||
| 700 | 0 | 1 | |a Poon Yiu Tung |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/16302/1/math_075_numb_001_002_289-297.pdf |z Dokumentum-elérés |