Numerical Radius Inequalities Concerning with Algebra Norms

Zamani, Ali; Moslehian, Mohammad Sal; Xu, Qingxiang; Fu, Chu-Li

doi:10.1007/s00009-020-01665-6

Cited by 15 publications

(9 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several results on the A-numerical radius have been established by many mathematicians, (see [6,8,12,13,14,20,22] and the references therein). ω A (•) defines a seminorm on B A 1/2 (H) which is equivalent to the A-operator seminorm • A .…”

Section: T X Amentioning

confidence: 99%

See 1 more Smart Citation

Generalized $A$-numerical radius of operators and related inequalities

Bhunia¹,

Feki²,

Paul³

2021

Preprint

View full text Add to dashboard Cite

Let A be a non-zero positive bounded linear operator on a complex Hilbert space (H, •, • ). Let ω A (T ) denote the A-numerical radius of an operator T acting on the semi-Hilbert space (H, •, • A ), where x, y A := Ax, y for all x, y ∈ H. Let N A (•) be a seminorm on the algebra of all A-bounded operators acting on H and let T be an operator which admits A-adjoint. Then, we define the generalized A-numerical radius aswhere T ♯A denotes a distinguished A-adjoint of T . We develop several generalized A-numerical radius inequalities from which follows the existing numerical radius and A-numerical radius inequalities. We also obtain bounds for generalized A-numerical radius of sum and product of operators. Finally, we study ω NA (•) in the setting of two particular seminorms N A (•).

show abstract

Section: T X Amentioning

confidence: 99%

“…It is easy to see that when N(•) = • , then ω N (•) coincides with the classical numerical radius w(•). The reader is invited to see [1,7,22] for intermediate properties and inequalities of the norm ω N (•). The main objective of this paper is to study the generalized numerical radius in the setting of semi-Hilbertian space operators.…”

Section: T X Amentioning

confidence: 99%

Generalized $A$-numerical radius of operators and related inequalities

Bhunia¹,

Feki²,

Paul³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Based on some operator theory studies on Hilbert spaces, several generalizations for the concept of numerical radius have recently been introduced [1,19,21]. Abu-Omar and Kittaneh [1] introduced the so-called generalized numerical radius: If M n denotes the space of all complex square matrices of size n, the generalized numerical radius for A, denoted by w N (A), is obtained via the supremum of the norm over the real parts of all rotations of A i.e.…”

Section: Introductionmentioning

confidence: 99%

“…]) that w(A) = sup θ∈R ∥ Re(e iθ A) ∥ . We refer the reader to [1,16,19] for intermediate properties and inequalities of the norm w N (.). In the present work, we restrict our attention to operator matrices A ∈ M n , where M n denotes the space of all complex square matrices.…”

Section: Introductionmentioning

confidence: 99%

Convexity and inequalities of some generalized numerical radius functions

Abbas

Harb²,

Issa

2022

Filomat

View full text Add to dashboard Cite

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).

show abstract

“…This concept is useful in studying linear operators and has attracted the attention of many authors in the last few decades (e.g., see [7,9,11,14,19,20,28], and their references).…”

Section: Introductionmentioning

confidence: 99%

The weighted Hilbert--Schmidt numerical radius

Zamani¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Let B(H) be the algebra of all bounded linear operators on a Hilbert space H and let N (•) be a norm on B(H). For every 0 ≤ ν ≤ 1, we introduce the w (N,ν) (A) as an extension of the classical numerical radius byand investigate basic properties of this notion and prove inequalities involving it. In particular, when N (•) is the Hilbert-Schmidt norm • 2 , we present several the weighted Hilbert-Schmidt numerical radius inequalities for operator matrices. Furthermore, we give a refinement of the triangle inequality for the Hilbert-Schmidt norm as follows:Our results extend some theorems due to F. .

show abstract

Numerical Radius Inequalities Concerning with Algebra Norms

Cited by 15 publications

References 12 publications

Generalized $A$-numerical radius of operators and related inequalities

Generalized $A$-numerical radius of operators and related inequalities

Convexity and inequalities of some generalized numerical radius functions

The weighted Hilbert--Schmidt numerical radius

Contact Info

Product

Resources

About