Related papers: Generalized Numerical Radius Inequalities for Scha…
We consider a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version that has been proposed in stochastic game theory. We establish an equivalence between this…
In this article, we developed a series of new inequalities involving the $q$-numerical radius for operators and $2\times 2$ operator matrices. These inequalities serve to establish both lower and upper bounds for the $q$-numerical radius of…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
We prove new inequalities for the essential generalized and the essential joint spectral radius of Hadamard (Schur) weighted geometric means of bounded sets of infinite nonnegative matrices that define operators on suitable Banach sequence…
The goal of this review is to explain some recent results regarding generalizations of the Stein-Tomas (and Strichartz) inequalities to the context of trace ideals (Schatten spaces).
In this paper, we study the relationship between operator space norm and operator space numerical radius on the matrix space $\mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. Moreover, we establish several inequalities for…
In this paper, we present the geometric Hardy inequalities on the starshaped sets in the Carnot groups. Also, we obtain the geometric Hardy inequalities on half-spaces for general vector fields.
We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this…
A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…
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…
We bring in some new notions associated with $2\times 2$ block positive semidefinite matrices. These notions concern the inequalities between the singular values of the off diagonal blocks and the eigenvalues of the arithmetic mean or…
In a recent work of the authors, we showed some general inequalities governing numerical radius inequalities using convex functions. In this article, we present results that complement the aforementioned inequalities. In particular, the new…
Let $\mathbb{B}(\mathcal{H})$ be the algebra of all bounded linear operators on a Hilbert space $\mathcal{H}$ and let $N(\cdot)$ be a norm on $\mathbb{B}(\mathcal{H})$. For every $0\leq \nu \leq 1$, we introduce the $w_{_{(N,\nu)}}(A)$ as…
In this article, we present new inequalities for the numerical radius of the sum of two Hilbert space operators. These new inequalities will enable us to obtain many generalizations and refinements of some well known inequalities, including…
In this paper, we achieve new and improved numerical radius inequalities of operators defined on a Hilbert space by using Orlicz function and Hermite-Hadamard inequality. The upper bounds of various inequalities involving numerical radii…
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…
Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for…
In this work, we discuss generalizations of the classical Bernstein and Markov type inequalities for polynomials and we present some new inequalities for the $k$th Fr\'echet derivative of homogeneous polynomials on real and complex…
In this article, we introduce several singular value and norm inequalities comparing the main diagonal and the off-diagonal components of a two by two PPT block. Some applications are given to obtain a new set of inequalities, some of which…
We consider the twin problems of estimating the effective rank and the Schatten norms $\|{\bf A}\|_{s}$ of a rectangular $p\times q$ matrix ${\bf A}$ from noisy observations. When $s$ is an even integer, we introduce a polynomial-time…