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...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
|
| Sorozat: | Acta scientiarum mathematicarum
75 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16302 |
| Tartalmi kivonat: | 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. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 289-297 |
| ISSN: | 0001-6969 |