berezin symbol
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scholarly journals Some upper bounds for the Berezin number of Hilbert space operators

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4353-4360
Author(s):  
Ali Taghavi ◽  
Tahere Roushan ◽  
Vahid Darvish
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Geometric Mean ◽  
Upper Bounds ◽  
Positive Definite ◽  
Berezin Symbol ◽  
Hilbert Space Operators ◽  
Positive Definite Operators ◽  
Berezin Number ◽  
Definition Of

In this paper, we obtain some Berezin number inequalities based on the definition of Berezin symbol. Among other inequalities, we show that if A,B be positive definite operators in B(H), and A#B is the geometric mean of them, then ber2(A#B) ? ber (A2+B2/2)- 1/2 inf ????(?k); where ?(?k?) = ?(A-B)?k?,?k??2, and ?k? is the normalized reproducing kernel of the space H for ? belong to some set.

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