berezin symbol
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Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4353-4360
Author(s):  
Ali Taghavi ◽  
Tahere Roushan ◽  
Vahid Darvish

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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