Inequalities for the Hadamard Weighted Geometric Mean of Positive Kernel Operators on Banach Function Spaces |
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Authors: | Roman Drnovšek Aljoša Peperko |
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Institution: | (1) Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia;(2) Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia |
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Abstract: | Let K1, . . . , Kn be positive kernel operators on a Banach function space. We prove that the Hadamard weighted geometric mean of K1, . . . , Kn, the operator K, satisfies the following inequalities
where || · ||and r(·) denote the operator norm and the spectral radius, respectively.
In the case of completely atomic measure space we show some additional results. In particular, we prove an infinite-dimensional
extension of the known characterization of those functions satisfying
for all non-negative matrices A1, . . . , An of the same order. |
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Keywords: | 47B34 47B65 47A10 47A12 47A63 |
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