Geodesic
A GENERALIZATION OF LEVINGER'S THEOREM TO POSITIVE KERNEL OPERATORS
Glasgow mathematical journal, Tome 45 (2003) no. 3, pp. 545-555

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DOI

We prove some inequalities for the spectral radius of positive operators on Banach function spaces. In particular, we prove the following extension of Levinger's theorem. Let $K$ be a positive compact kernel operator on $L^2(X, \mu)$ with the spectral radius $r(K)$. Then the function $\phi$ defined by $\phi(t) = r(t K + (1-t) K^*)$ is non-decreasing on $[0, \frac{1}{2}]$. We also prove that $\| A + B^* \| \ge 2 \cdot \sqrt{r(A B)}$ for any positive operators $A$ and $B$ on $L^2(X, \mu)$.
DOI : 10.1017/S0017089503001459
Mots-clés : 47B34, 47B65, 47A10, 47A12, 47A63 
DRNOVšEK, ROMAN. A GENERALIZATION OF LEVINGER'S THEOREM TO POSITIVE KERNEL OPERATORS. Glasgow mathematical journal, Tome 45 (2003) no. 3, pp. 545-555. doi: 10.1017/S0017089503001459
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     title = {A {GENERALIZATION} {OF} {LEVINGER'S} {THEOREM} {TO} {POSITIVE} {KERNEL} {OPERATORS}},
     journal = {Glasgow mathematical journal},
     pages = {545--555},
     year = {2003},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001459/}
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