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- W4360614575 abstract "The Berezin transform $widetilde{A}$ and the Berezin number of an operator $A$ on the reproducing kernel Hilbert space over some set $Omega$ with normalized reproducing kernel $widehat{k}_{lambda}$ are defined, respectively, by $widetilde{A}(lambda)=leftlangle {A}widehat{k}_{lambda },widehat{k}_{lambda}rightrangle , lambdainOmega$ and $mathrm{ber}% (A):=sup_{lambdainOmega}leftvert widetilde{A}{(lambda)}rightvert .$ A straightforward comparison between these characteristics yields the inequalities $mathrm{ber}left( Aright) leqfrac{1}{2}left( leftVert ArightVert _{mathrm{ber}}+leftVert A^{2}rightVert _{mathrm{ber}}% ^{1/2}right) $. In this paper, we study further inequalities relating them. Namely, we obtained some refinement of Berezin number inequalities involving convex functions. In particular, for $Ainmathcal{B}left( mathcal{H}% right) $ and $rgeq1$ we show that [ mathrm{ber}^{2r}left( Aright) leqfrac{1}{4}left( leftVert A^{ast }A+AA^{ast}rightVert _{mathrm{ber}}^{r}+leftVert A^{ast}A-AA^{ast }rightVert _{mathrm{ber}}^{r}right) +frac{1}{2}mathrm{ber}^{r}left( A^{2}right) . ]" @default.
- W4360614575 created "2023-03-24" @default.
- W4360614575 creator A5026788248 @default.
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- W4360614575 date "2023-03-30" @default.
- W4360614575 modified "2023-09-30" @default.
- W4360614575 title "Some refinements of Berezin number inequalities via convex functions" @default.
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- W4360614575 doi "https://doi.org/10.31801/cfsuasmas.1089790" @default.
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