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In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]

In this work, we give several new upper and lower bounds for the p-numerical radii of operators as well as for n × n operator matrices. An application to 2-nilpotent operators is provided, and a p-numerical radius power inequality is also given. [ABSTRACT FROM AUTHOR]

We present several upper bounds for the numerical radii of 2 × 2 operator matrices. We employ these bounds to improve on some known numerical radius inequalities for powers of Hilbert space operators. In particular, we show that if T is a bounded linear operator on a complex Hilbert space, then for every r ≥ 1 and α ∈ [0, 1]. This substantially improves on the existing inequality. Here w(.) and ||.|| denote the numerical radius and the usual operator norm, respectively. [ABSTRACT FROM AUTHOR]

We give some new bounds for the numerical radii of the off-diagonal parts of 2 × 2 operator matrices. A refinement of the triangle inequality for the operator norm is also given. [ABSTRACT FROM AUTHOR]

Extending certain scalar and norm inequalities, we present new inequalities for the numerical radius, which generalize and refine some known results. Applications of the obtained inequalities include a new original proof of the matrix arithmetic-geometric mean inequality and certain extensions of some well-established results from the literature for products of matrices. [ABSTRACT FROM AUTHOR]

Let A be a bounded linear operator defined on a complex Hilbert space and let | A | = (A * ⁢ A) 1 2 . Among other refinements of the well-known numerical radius inequality w 2 ⁢ (A) ≤ 1 2 ⁢ ∥ A * ⁢ A + A ⁢ A * ∥ , we show that w 2 ⁢ (A) ≤ 1 4 ⁢ w 2 ⁢ (| A ⁢ | + i | ⁢ A * |) + 1 8 ⁢ ∥ | A | 2 + | A * | 2 ∥ + 1 4 ⁢ w ⁢ (| A | ⁢ | A * |) ≤ 1 2 ⁢ ∥ A * ⁢ A + A ⁢ A * ∥ . Also, we develop inequalities involving the numerical radius and the spectral radius for the sum of the product operators, from which we derive the inequalities w p ⁢ (A) ≤ 1 2 ⁢ w ⁢ ( | A | p + i ⁢ | A * | p ) ≤ ∥ A ∥ p for all p ≥ 1 . Further, we derive new bounds for the zeros of complex polynomials. [ABSTRACT FROM AUTHOR]

The two well-known numerical radius inequalities for the tensor product A ⊗ B acting on H ⊗ K , where A and B are bounded linear operators defined on complex Hilbert spaces H and K , respectively are 1 2 ‖ A ‖ ‖ B ‖ ≤ w (A ⊗ B) ≤ ‖ A ‖ ‖ B ‖ and w (A) w (B) ≤ w (A ⊗ B) ≤ min { w (A) ‖ B ‖ , w (B) ‖ A ‖ }. In this article, we develop new lower and upper bounds for the numerical radius w (A ⊗ B) of the tensor product A ⊗ B and study the equality conditions for those bounds. [ABSTRACT FROM AUTHOR]

Let (H, 〈 · , · 〉) be a complex Hilbert space and A be a positive bounded linear operator on H. The semi-inner product 〈x, y〉A: = 〈Ax, y〉, x, y ∈ H, induces a semi-norm ∥ ⋅ ∥ A on H. Let ωA(T) and ∥ T ∥ A denote the A-numerical radius and the A-operator semi-norm of an operator T in semi-Hilbertian space (H, 〈 · , · 〉A), respectively. In this paper, some new bounds for the A-numerical radius of operators in semi-Hilbertian space are obtained, which improve the existing ones. In particular, a refinement of the triangle inequality for A-operator semi-norm is also shown. [ABSTRACT FROM AUTHOR]

In this paper, we firstly establish new numerical radius inequalities which refine a result of Kittaneh in [Studia Math. 168, 73–80 (2005)], then present some numerical radius inequalities involving non-negative increasing convex functions for n × n operator matrices, which generalize the related results of Shebrawi in [Linear Algebra Appl. 523(15), 1–12 (2017)]. [ABSTRACT FROM AUTHOR]

In this paper, we establish some numerical radius inequalities for 2 × 2 bounded linear operator defined on a complex Hilbert space. As a natural application, the existence of the all polynomial zeros is identified in a specific small disk. Moreover, we provide a refinement of an earlier numerical radius inequality due to Herzallah et al. [Numerical radius inequalities for certain 2 × 2 operator matrices. Integr Equ Oper Theory. 2011;71:129–147] and a generalization of Shebrawi's inequality [Numerical radius inequalities for certain 2 × 2 operator matrices II. Linear Algebra Appl. 2017;523:1–12]. [ABSTRACT FROM AUTHOR]

In this article, we consider the condition pseudospectrum of bounded linear operators on a Banach space. The condition pseudospectrum of normal matrices and Jordan blocks are characterized and condition pseudospectral radius of the classes are found. Sub-additivity and sub-multiplicativity of the condition pseudospectral radius for commuting pairs of bounded linear operators are proved. It is shown that the condition pseudospectral radius becomes a complete algebra norm in a commutative complex unital Banach algebra. Certain examples are given to illustrate the results. The results developed are also extended to a general setting. [ABSTRACT FROM AUTHOR]

The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in the literature. In this article, we present many new inequalities for the numerical radius of accretive matrices. The importance of this study is the presence of a new approach that treats a specific class of matrices, namely the accretive ones. While some of these inequalities can be considered as refinements of other existing ones, others present new insight to some known results for positive matrices. [ABSTRACT FROM AUTHOR]

New numerical radius inequalities for Hilbert space operators are given. These inequalities improve a well-known inequality of F. Kittaneh. We also show that the inequalities obtained here are sharp. A refinement of the triangle inequality is also shown. [ABSTRACT FROM AUTHOR]

In this work, we provide upper and lower bounds for the numerical radius of an n × n off-diagonal operator matrix, which extends some results by Abu-Omar and Kittaneh (Stud. Math. 216:69–75, 2013; Linear Algebra Appl. 468:18–26, 2015; Rocky Mt. J. Math. 45(4):1055–1065, 2015), and Paul and Bag (Appl. Math. Comput. 222:2731–2943, 2013). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space H when an additional semi-inner product induced by a positive operator A is considered. We investigate this new class of operators which is called A-normal d-tuple of operators. Mainly, we study the tensor product and the tensor sum of two A-normal d-tuples of operators. Also, we define the A-joint spectral radius associated with a d-tuple T = (T 1 , ... , T d) denoted r A (T) and we show that under some conditions we have r A (T) = | | | T | | | A , where | | | T | | | A denotes the A-joint operator seminorm of T . [ABSTRACT FROM AUTHOR]

The aim of this article is to prove several new numerical radius inequalities for n × n operator matrices on a Hilbert space. Let be complex Hilbert spaces, and let be an n × n operator matrix with. Among other inequalities, it shown that where and denote the numerical radius and the usual operator norm, respectively. [ABSTRACT FROM AUTHOR]

Let v(x) denote the numerical radius of an element x in a C ∗ -algebra A . First, we prove several numerical radius inequalities in A . Particularly, we show that if x ∈ A , then v (x) = 1 2 ‖ x ‖ if and only if ‖ x ‖ = ‖ Re (e i θ x) ‖ + ‖ Im (e i θ x) ‖ for all θ ∈ R . In addition, we present a refinement of the triangle inequality for the numerical radius in C ∗ -algebras. Among other things, we introduce a new type of parallelism in the setting of C ∗ -algebras based on the notion of numerical radius. More precisely, an element x ∈ A is called the numerical radius parallel to another element y ∈ A , denoted by x ‖ v y , if v (x + λ x) = v (x) + v (y) for some complex unit λ . We show that this relation can be characterized in terms of pure states acting on A . [ABSTRACT FROM AUTHOR]

The main goal of this article is to present numerical radius inequalities for matrices based on convexity of certain numerical radius functions. This simple approach extends some unitarily invariant norms inequalities, such as Heinz and Young inequalities, to the context of numerical radius. However, due to weak unitary invariance of the numerical radius, these extended inequalities will be weaker than the corresponding unitarily invariant norms versions. [ABSTRACT FROM AUTHOR]

We give several sharp numerical radius inequalities for certain 2 × 2 operator matrices. Among other inequalities, it is shown that if A and B be operators in B ( H ) . Then w ( [ A B 0 0 ] ) ≤ 1 2 ( ‖ A ‖ + ‖ A A ⁎ + B B ⁎ ‖ 1 2 ) and 2 w ( [ 0 A B 0 ] ) ≤ max ⁡ ( ‖ A ‖ , ‖ B ‖ ) + 1 2 ( ‖ | A | t | B ⁎ | 1 − t ‖ + ‖ | B | t | A ⁎ | 1 − t ‖ ) for all t ∈ [ 0 , 1 ] , where w ( ⋅ ) and ‖ ⋅ ‖ denote the numerical radius and the usual operator norm, respectively. The second inequality refines and generalizes earlier inequalities. [ABSTRACT FROM AUTHOR]

In this paper we give several expressions of spectral radius of a bounded operator on a Hilbert space, in terms of iterated λ -Aluthge transform, numerical radius and the asymptotic behavior of the powers of this operator. We also obtain several characterizations of normaloid operators. [ABSTRACT FROM AUTHOR]

We show that if T = H + i K is the Cartesian decomposition of T ∈ B ( H ) , then for α , β ∈ R , sup α 2 + β 2 = 1 ⁡ ‖ α H + β K ‖ = w ( T ) . We then apply it to prove that if A , B , X ∈ B ( H ) and 0 ≤ m I ≤ X , then m ‖ Re ( A ) − Re ( B ) ‖ ≤ w ( Re ( A ) X − X Re ( B ) ) ≤ 1 2 sup θ ∈ R ⁡ ‖ ( A X − X B ) + e i θ ( X A − B X ) ‖ ≤ ‖ A X − X B ‖ + ‖ X A − B X ‖ 2 , where Re ( T ) denotes the real part of an operator T . A refinement of the triangle inequality is also shown. [ABSTRACT FROM AUTHOR]