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This paper presents several Berezin number and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. Among other inequali- ties, it is shown that if A is a bounded linear operator on a Hilbert space, then ... where R = max{t, 1-t} and 0 ≤ t ≤ 1. [ABSTRACT FROM AUTHOR]

In this paper, we improve some numerical radius inequalities for Hilbert space operators under suitable condition. We also compare our results with some known results. As application of our result, we obtain an operator inequality.

This article considers the class of convex functions and derives further Jensen-Mercer'stype inequalities. The obtained results improve and generalize some known inequalities. A reverse of Jesnen-Mercer's inequality for scalars and operators is also given. As an application, we provide a new and non-trivial inequality related to the Wigner-Yanase-Dyson function and the logarithmic mean. [ABSTRACT FROM AUTHOR]

In this paper by using the notion of sesquilinear form we introduce a new class of numerical range and numerical radius in normed space 𝒱, also its various characterizations are given. We apply our results to get some inequalities.

Some operator inequalities for synchronous functions that are related to the čebyšev inequality are given. Among other inequalities for synchronous functions it is shown that ∥ø(f(A)g(A)) - ø(f(A))ø(g(A))∥ ≤ max{║ø(f2(A)) - ø2(f(A))║, ║ø)G2(A)) - ø2(g(A))║} where A is a self-adjoint and compact operator on B(ℋ ), f, g ∈ C (sp (A)) continuous and non-negative functions and ø: B(ℋ ) → B(ℋ ) be a n-normalized bounded positive linear map. In addition, by using the concept of quadruple D-synchronous functions which is generalizes the concept of a pair of synchronous functions, we establish an inequality similar to čebyšev inequality.

In this paper, we obtain some sharp inequalities for numerical radius of finite sums of operators. Moreover, we give some applications of our result in estimation of spectral radius. We also compare our results with some known results.

New numerical radius inequalities for Hilbert space operators are given. We give an improvement of the inequality presented by Kittaneh for numerical radius, in fact we show that if A ∈ ℬ (ℋ) , then ω (A) ≤ 1 2 ∥ | A | + | A ∗ | ∥ − 1 2 inf ∥ x ∥ = 1 ϕ (x) , where ϕ (x) = inf { (〈 | A | x , x 〉 1 2 − 〈 | A ∗ | x , x 〉 1 2 ) 2 : ∥ x ∥ = 1 }. A refinement of the triangle inequality is also shown. [ABSTRACT FROM AUTHOR]

In this paper, we present a refinement of the well-known arithmetic-geometric mean inequality. As application of our result, we obtain an operator inequality. We give an improvement of the inequality presented by Kittaneh for the numerical radius. [ABSTRACT FROM AUTHOR]

We give a new lower bound in some inequalities for frames in a Hilbert space. If fiiI is a Parseval frame for the Hilbert space H with frame operator Sf = P iI f, fifi, then, for every J I and f H, we have some improvements of the inequalities for general frames and alternate dual frames under suitable conditions. Our results refine the remarkable results obtained by Balan et al. and Gavruta. [ABSTRACT FROM AUTHOR]

We extend some numerical radius inequalities for adjointable operators on Hilbert C*-modules. A new refinement of a numerical radius inequality for some Hilbert space operators is given. More precisely, we prove that if T ∈ ℬ ⁢ (ℋ) is an invertible operator, then ∥T∥/2 ≤ √∥T∥2 + 1/∥T−1∥2/2 ≤ ω(T). [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]

This paper dedicated to study quadratic maps. We present some new operator equalities and inequalities by using quadratic map in the frame-work of B (H). Applications for particular case of interest are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we have obtained the analogue results on numerical radius inequalities from the classical inner product spaces to 2-inner product spaces. We have established several related reverse inequalities and some well known results in 2-inner product spaces. [ABSTRACT FROM AUTHOR]

In this paper, the definition Rhombic numerical radius is introduced and we present several numerical radius inequalities. Some applications of these inequalities are considered as well. Particular, it is shown that, if A ∈ B(H) with the Cartesian decomposition A = C + iD and r ≥ 1, then ... [ABSTRACT FROM AUTHOR]

We improve and generalize some operator inequalities for positive linear maps. It is shown, among other inequalities, that if or , then for each and , and where , and . We also obtain an improvement of operator Pólya-Szegö inequality. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some sharp inequalities for numerical radius of finite sums of operators. Moreover, we give some applications of our result in estimation of spectral radius. We also compare our results with some known results. [ABSTRACT FROM AUTHOR]

We establish an operator extension of the following inequality, due to Cartwright and Field .... Applications of this inequality for self-adjoint operators, continuous fields of operators and unital fields of positive linear mapping are also given. [ABSTRACT FROM AUTHOR]

We obtain some sharp inequalities for essential numerical radius we (.) of operators. Moreover, we give some applications of our results in estimation of essential norm, and compare our results with some usual norm known results. In particular, we obtain under suitable conditions if T 2 B (H), then w (T) ≤ǁTǁ ≤ ǁTǁ. [ABSTRACT FROM AUTHOR]

By using sesquilinear map we generalize some operator Kantorovich inequalities. Our results are more extensive than many previous results due to Mond and Pečarić. [ABSTRACT FROM AUTHOR]

In this paper we present some new operator inequality for convex functions. We have obtained a number of Jensen's type inequalities for convex and operator convex functions of self-adjoint operators for positive linear maps. Some results are exemplified for power and logarithmic functions. [ABSTRACT FROM AUTHOR]

We introduce the concept of operator φ-convex and obtain some Hermite-Hadamard type inequalities for these class of functions for positive linear maps. As applications, we obtain several singular value inequalities for operators. [ABSTRACT FROM AUTHOR]