Numerical Radius Inequalities for Certain 2 × 2 Operator Matrices

By Omar Hirzallah, F. Kıttaneh, K. Shebrawi. 2011

169 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4240fce2096e41c888512935057ed1751e480963

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In Applied Mathematics

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Citations in the corpus

Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces (2019, background): “that if T is A-selfadjoint (or A-normal), then wA(T) = kTkA. For proofs and more facts about A-numerical radius of operators, we refer the reader to [5, 18]. Some other related topics can be found in [1, 2, 3, 4, 8, 9, 10, 11, 12, 13, 15, 17]. In Section 2, we discuss some useful seminorm inequaliti”
Cartesian decomposition and Numerical radius inequalities (2015, background): “B 0 0 #! = kAX−XBk 2 and w " 0 0 A∗X − XB∗ 0 #! = kA∗X−XB∗k 2 . It should be mentioned here that (2.5) follows as a special case of (2.6) by recalling that w " 0 C C 0 #! = w(C) (see, e.g., [10]). It follows from Corollary 5 in [3] that if U,V ∈ B(H ) are unitary and 0 < mI ≤ X for some”
Some improvements of numerical radius inequalities of operators and operator matrices (2019, background): “econd author would like to thank RUSA 2.0, Jadavpur University for the partial support. 1 2 PINTUBHUNIAANDKALLOLPAUL Various numerical radius inequalities improving this inequality have been given in [3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20]. We reserve the alphabets I and O for identity o”
A-numerical radius inequalities for semi-Hilbertian space operators (2019, background): “btained by several mathematicians (see, e.g., [1, 2, 10, 16, 21, 23, 32, 33]). Motivated by theoretical study and applications, there have been many generalizations of the numerical radius (e.g., see [3, 6, 9, 15, 17, 19, 20, 26, 27, 28, 29, 34]). One of these generalizations is the A-numerical radi”
Numerical radius inequalities for 2 × 2 operator matrices (2012, methodology): “Now, we need the following lemma, which has also been used in [9] and [10].”