Related papers: Operator inequalities related to weak 2-positivity
We discuss the reflexivity of hyperexpansions and their Cauchy dual operators. In particular, we show that any cyclic completely hyperexpansive operator is reflexive. We also establish the reflexivity of the Cauchy dual of an arbitrary…
One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known…
In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Acz\'{e}l inequality and its reverse via…
In this paper, we obtained the Dunkl analogy of classical Lp Hardy inequality for $p > N + 2\gamma$ with sharp constant $\left(\frac{p-N-2\gamma}{p}\right)^{p}$, where $2\gamma$ is the degree of weight function associated with Dunkl…
We introduce and systematically develop the theory of \emph{quantum doubly stochastic operators}, i.e. positive, trace-preserving maps on non-commutative $L_p$-spaces associated to semifinite von Neumann algebras. After establishing basic…
We classify weakly Einstein submanifolds in space forms that satisfy Chen's equality. We also give a classification of weakly Einstein hypersurfaces in space forms that satisfy the semisymmetric condition. In addition, we discuss some…
The Schr{\"o}dinger inequality is known to underlie the Kennard-Robertson inequality, which is the standard expression of quantum uncertainty for the product of variances of two observables $A$ and $B$, in the sense that the latter is…
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
In this paper we present several applications of Cartwright-Field's inequality. Among these we found Young's inequality, Bernoulli's inequality, the inequality between the weighted power means, H\"{o}lder's inequality and Cauchy's…
We show that a weighted manifold which admits a relative Faber Krahn inequality admits the Fefferman Phong inequality V $\psi$, $\psi$ $\le$ CV $\psi$ 2 , with the constant depending on a Morrey norm of V , and we deduce from it a condition…
Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…
M. Lin defined a binary operation for two positive semi-definite matrices in studying certain determinantal inequalities that arise from diffusion tensor imaging. This operation enjoys some interesting properties similar to the operator…
In this paper, a generalized Cauchy-Schwarz inequality for positive sesquilinear maps with values in noncommutative Lp-spaces for p > 1 are obtained. Bound estimates for their real and imaginary parts are also provided, and, as an…
We consider operators T : M_0 -> Z and T : M -> Z, where Z is a Banach space and (M_0, M) is a pair of Banach spaces belonging to a general construction in which M is defined by a "big-O" condition and M_0 is given by the corresponding…
In this paper we introduce the concept of quadratic operator perspective for a continuous function {\Phi} defined on the positive semi-axis of real numbers. This generalize the quadratic weighted operator geometric mean and the quadratic…
A theorem of Davis, Figiel, Johnson and Pe{\l}czy\'nski tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method,…
For a class of linear maps on a von Neumann factor, we associate two objects, bounded operators and trace class operators, both of which play the roles of Choi matrices. Each of them is positive if and only if the original map on the factor…
We find the exact values for constants in bilateral Calderon-Stein-Weiss inequalities between tail (Marcinkiewicz) norm and weak Lebesgue (Lorentz) norm. Possible applications: Functional Analysis (for instance, interpolation of operators),…
We study $\omega$-weak equivalences between weak $\omega$-categories in the sense of Batanin-Leinster. Our $\omega$-weak equivalences are strict $\omega$-functors satisfying essential surjectivity in every dimension, and when restricted to…
This work focuses on the nonhomogeneous nonlocal double phase problem \begin{align*} L_au(x)=f(x,u,D_s^p u, D_{a,t}^q u) \text{ in } \Omega, \end{align*} where $\Omega\subset\mathbb{R}^N$ is a bounded domain with Lipschitz boundary,…