Related papers: Operator inequalities related to weak 2-positivity
We characterize a four-weight inequality involving the Hardy operator and the Copson operator. More precisely, given $p_1, p_2, q_1, q_2 \in (0, \infty)$, we find necessary and sufficient conditions on nonnegative measurable functions $u_1,…
Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize validity of the inequality for the composition of the Hardy operator, \begin{equation*} \bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt \bigg)^{\frac{r}{q}}…
The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea…
We review some of the significant generalizations and applications of the celebrated Douglas theorem on the equivalence of factorization, range inclusion, and majorization of operators. We then apply it to find a characterization of the…
Our purpose in this note is to investigate the order properties of positive operators from a locally convex space into its conjugate dual. We introduce a natural generalization of the Busch-Gudder strength function and we prove Kadison's…
We square operator P\'{o}lya--Szeg\"{o} and Diaz--Metcalf type inequalities as follows: If operator inequalities $0<m_{1}^{2} \leq A\leq M_{1}^{2}$ and $0<m_{2}^{2}\leq B\leq M_{2}^{2}$ hold for some positive real numbers $m_{1}\leq M_{1}$…
L- and M-weakly compact operators were introduced by Meyer-Nieberg in the beginning of seventies in attempts of a diversification of the concept of weakly compact operators via imposing Banach lattice structure on the range or on the domain…
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
In a filtered measure space, a characterization of weights for which the trace inequality of a positive operator holds is given by the use of discrete Wolff's potential. A refinement of the Carleson embedding theorem is also introduced.…
Some Ostrowski type inequalities via Cauchy's mean value theorem and applications for certain particular instances of functions are given.
In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They…
We introduce the forward (backward) gH-difference operator of interval sequences, and establish some new discrete Opial type inequalities for interval-valued functions. Further, we obtain generalizations of classical discrete Opial type…
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
The paper concentrates on the application of the following Hardy inequality \begin{equation*} \int_\Omega \ |\xi(x)|^p \omega_{1 }(x)dx\le \int_\Omega |\nabla \xi(x)|^p\omega_{2 }(x)dx, \end{equation*} to the proof of existence of weak…
Weak measurements are a new tool for characterizing post-selected quantum systems during their evolution. Weak measurement was originally formulated in terms of von Neumann interactions which are practically available for only the simplest…
We announce a new type of "Jacobi identity" for vertex operator algebras, incorporating values of the Riemann zeta function at negative integers. Using this we "explain" and generalize some recent work of S. Bloch's relating values of the…
We introduce new class of limitedly L-weakly compact operators from a Banach space to a Banach lattice. This class is a proper subclass of the Bourgain-Diestel operators and it contains properly the class of L-weakly compact operators. We…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…
A weak invariant associated with a master equation is characterized in such a way that its spectrum is not constant in time but its expectation value is conserved under time evolution generated by the master equation. Here, an intriguing…