Geodesic
The A-Davis-Wielandt Berezin number of semi Hilbert operators with some related inequalities
Filomat, Tome 37 (2023) no. 12, p. 3837

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DOI

In this article, the concept of the A-Davis-Wielandt Berezin number is introduced for positive operator A. Some upper and lower bounds for the A-Davis-Wielandt Berezin number are proved. Moreover, some inequalities related to the concept of the Davis-Wielandt Berezin number are obtained, which are generalizations of known results. Among them, it is shown that ber 2 dw (S) ≤ inf γ∈C { 2||Re(γ)Re(S) + Im(γ)Im(S)|| + ||S * S − 2Re(¯ γS)|| 2 + 2||Re(¯ γS)|| − |γ| 2 + ber 2 (S − γI)}, where S ∈ B(H(Ω)). Also, we determined the exact value of the A-Davis-Wielandt Berezin number of some special type of operator matrices.
DOI : 10.2298/FIL2312837G
Classification : 47A30, 47A12, 47A63, 47L05
Keywords: A- Berezin number, A-Davis-Wielandt Berezin number, Davis-Wielandt Berezin number, Berezin number, 2×2 operator matrix, Semi Hilbert space 
Fatemeh Goli; Rahmatollah Lashkaripour; Monire Hajmohamadi. The A-Davis-Wielandt Berezin number of semi Hilbert operators with some related inequalities. Filomat, Tome 37 (2023) no. 12, p. 3837 . doi: 10.2298/FIL2312837G
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     author = {Fatemeh Goli and Rahmatollah Lashkaripour and Monire Hajmohamadi},
     title = {The {A-Davis-Wielandt} {Berezin} number of semi {Hilbert} operators with some related inequalities},
     journal = {Filomat},
     pages = {3837 },
     year = {2023},
     volume = {37},
     number = {12},
     doi = {10.2298/FIL2312837G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312837G/}
}
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