Norm and numerical radius inequalities for Hilbert space operators

Bani-Domi, Watheq; Kittaneh, Fuad

doi:10.1080/03081087.2020.1798334

Cited by 23 publications

(5 citation statements)

References 13 publications

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“…And therefore, w 2 p (X) ≥ Remark First note that the majority of the inequalities and results provided in this paper, can be extended to B(H), the space of all bounded linear operators on a complex separable Hilbert space H. Second a further investigation could be done to find an upper bound for the Schatten p−generalized numerical radius for partitioned 2 × 2 block matrices by using some ideas for [6,22].…”

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confidence: 93%

Convexity and inequalities of some generalized numerical radius functions

Abbas

Harb²,

Issa

2022

Filomat

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In this paper, we prove that each of the following functions is convex on R: f(t) = wN(AtXA1?t ? A1?tXAt), g(t) = wN(AtXA1?t), and h(t) = wN(AtXAt) where A > 0, X ? Mn and N(.) is a unitarily invariant norm onMn. Consequently, we answer positively the question concerning the convexity of the function t ? w(AtXAt) proposed by in (2018). We provide some generalizations and extensions of wN(.) by using Kwong functions. More precisely, we prove the following wN(f(A)X1(A) + g(A)Xf (A)) ? wN(AX+XA) ? 2wN(X)N(A), which is a kind of generalization of Heinz inequality for the generalized numerical radius norm. Finally, some inequalities for the Schatten p-generalized numerical radius for partitioned 2 ? 2 block matrices are established, which generalize the Hilbert-Schmidt numerical radius inequalities given by Aldalabih and Kittaneh in (2019).

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confidence: 93%

Convexity and inequalities of some generalized numerical radius functions

Abbas

Harb²,

Issa

2022

Filomat

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“…In this study, the upper bounds of the Berezin radius inequalities of 2×2 operator matrices were found. Al-Dolat and Kittaneh ( [2]) and Bani-Domi and Kittaneh ( [7]) inequalities are shown for 2 × 2 operator matrices using auxiliary theorems.…”

Section: Introduction Manymentioning

confidence: 99%

“…The numeric range of an operator has some interesting properties, such as the closure of the numeric range of an operator's spectrum. For basic information about this theory, we can give [1,2,3,7,17] and its references.…”

Section: Introduction Manymentioning

confidence: 99%

Application of Operator Matrices of 2x2 of Berezin Radius Inequality

2023

Proceeding Book of 1st International Conference on Recent and Innovative Results in Engineering and Technology Icriret 2023

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Many researchers in mathematics and mathematical physics are working on the Berezin symbol of the core Hilbert space operator, which has been proliferating in recent years. In this direction, some researchers (1.2) continued their important studies on the Berezin inequality ([18-24]). As a matter of fact, improved and improved versions of this inequality have attracted the attention of researchers in recent years ([8-11]. In this study, the upper bounds of the Berezin radius inequalities of 2 × 2 operator matrices were found. ) and ) inequalities are shown for 2 × 2 operator matrices using auxiliary theorems.

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“…Several new norms and numerical radius inequalities for 2 × 2 block operator matrices have been researched in [9]. Recently, several new A-numerical radius inequalities for many type n × n block operator matrices have been offered in [9] in the direct sum of Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%