Geodesic
Refined Berezin number inequalities via superquadratic and convex functions
Filomat, Tome 37 (2023) no. 1, p. 265

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DOI

In this paper, we generalize and refine some Berezin number inequalities for Hilbert space operators. Namely, we refine the Hermite-Hadamard inequality and some other recent results by using the concept of superquadraticity and convexity. Then we extend these inequalities for the Berezin number. Among other inequalities, it is shown that if S, T ∈ L(H(Ω)) such that ber(T) ≤ ber(|S|) and f is a non-negative superquadratic function, then f (ber (T)) ≤ ber(f (|S|)) − ℓ ber f (||S| − ber (T)|) .
DOI : 10.2298/FIL2301265C
Classification : 47A63, 15A60
Keywords: Berezin number, Berezin symbol, Positive operator, Young inequality, Hölder-McCarthy’s inequality, Ando’s inequality 
Fengsheng Chien; Mojtaba Bakherad; Mohammad W Alomari. Refined Berezin number inequalities via superquadratic and convex functions. Filomat, Tome 37 (2023) no. 1, p. 265 . doi: 10.2298/FIL2301265C
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     title = {Refined {Berezin} number inequalities via superquadratic and convex functions},
     journal = {Filomat},
     pages = {265 },
     year = {2023},
     volume = {37},
     number = {1},
     doi = {10.2298/FIL2301265C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2301265C/}
}
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