Geodesic
On the inequality w(AB) ≤ c∥A∥w(B) where A is a positive operator
Filomat, Tome 36 (2022) no. 4, p. 1337

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Abu-Omar and Kittaneh [Numerical radius inequalities for products of Hilbert space operators, J. Operator Theory 72(2) (2014), 521–527], wonder what is the smallest constant c such that w(AB) ≤ c∥A∥w(B) for all bounded linear operators A, B on a complex Hilbert space with A is positive. Here, w(·) stands for the numerical radius. In this paper, we prove that c = ̲3̲√̲3̲ ꜭ
DOI : 10.2298/FIL2204337B
Classification : 47A10, 47A12, 47A30
Keywords: Numerical radius, Numerical radius inequalities, Numerical range 
El Hassan Benabdi; Abderrahim Baghdad; Mohamed Chraibi Kaadoud; Mohamed Barraa. On the inequality w(AB) ≤ c∥A∥w(B) where A is a positive operator. Filomat, Tome 36 (2022) no. 4, p. 1337 . doi: 10.2298/FIL2204337B
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     title = {On the inequality {w(AB)} \ensuremath{\leq} {c\ensuremath{\parallel}A\ensuremath{\parallel}w(B)} where {A} is a positive operator},
     journal = {Filomat},
     pages = {1337 },
     year = {2022},
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     doi = {10.2298/FIL2204337B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2204337B/}
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