Abstract
A Hardy type inequality for Reproducing Kernel Hilbert Space operators is proved. It is well known (see Halmos in A Hilbert space problem book. Springer, Berlin, 1982) the following power inequality for numerical radius of Hilbert space operator A:
for any integer \(n>0\). Hovewer, the inverse inequalities
for some operator classes with some constant \(C=C\left( n\right) >1\), apparently, are not well investigated in the literature. The same inequalities for the Berezin number of operators on the reproducing Kernel Hilbert space are not studied in general. Here we prove some power inequalities for Berezin number of some operators.
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The authors thank the referee for his useful remarks and suggestions which improved the presentation of the paper.
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This paper was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center. Also, the second author is supported by TUBA through Young Scientist Award Program (TUBA-GEBIP/2015).
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Garayev, M.T., Gürdal, M. & Saltan, S. Hardy type inequaltiy for reproducing Kernel Hilbert space operators and related problems. Positivity 21, 1615–1623 (2017). https://doi.org/10.1007/s11117-017-0489-6
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DOI: https://doi.org/10.1007/s11117-017-0489-6