Geometrical significance of the löwner-heinz inequality
It is proven that the Lowner-Heinz inequality ||At Bt|| ≤ ||AB||t, valid for all positive invertible operators A, B on the Hubert space H and t ε [0, 1], has equivalent forms related to the Finsler structure of the space of positive invertible elements of L(H) or, more generally, of a unital C*-alge...
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| Autores principales: | , , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00029939_v128_n4_p1031_Andruchow |
| Aporte de: |
| Sumario: | It is proven that the Lowner-Heinz inequality ||At Bt|| ≤ ||AB||t, valid for all positive invertible operators A, B on the Hubert space H and t ε [0, 1], has equivalent forms related to the Finsler structure of the space of positive invertible elements of L(H) or, more generally, of a unital C*-algebra. In particular, the Löwner-Heinz inequality is equivalent to some type of "nonpositive curvature" property of that space. © 2000 American Mathematical Society. |
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