Bhatia, Rajendra ; Sano, Takashi (2009) Positivity and conditional positivity of Loewner matrices Positivity . ISSN 1385-1292
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Official URL: http://www.springerlink.com/index/X1316J980240W785...
Related URL: http://dx.doi.org/10.1007/s11117-009-0027-2
Abstract
We give elementary proofs of the fact that the Loewner matrices [f(pi)-f(pj)/pi-pj]corresponding to the function f(t) = t r on (0, ∞ ) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0, ∞ ) the Loewner matrices corresponding to an operator convex function on (-1, 1) need not be conditionally negative definite.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer-Verlag. |
| Keywords: | Loewner Matrix; Operator Monotone; Operator Convex; Positive Semidefinite; Conditionally Positive Definite; Conditionally Negative Definite |
| ID Code: | 2528 |
| Deposited On: | 08 Oct 2010 07:01 |
| Last Modified: | 08 Oct 2010 07:01 |
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