Refined Jensen's operator inequality with condition on spectra

This is a submission to one of journals of TMRG: BJMA/AFA EXTENSION OF THE REFINED JENSEN’S OPERATOR INEQUALITY WITH CONDITION ON SPECTRA

We give an extension of the refined Jensen’s operator inequality for n−tuples of self-adjoint operators, unital n−tuples of positive linear mappings and real valued continuous convex functions with conditions on the spectra of the operators. We also study the order among quasi-arithmetic means under similar conditions.

An Extension of Chebyshevs Inequality and Its Connection with Jensens Inequality

The aim of this paper is to show that Jensen’s Inequality and an extension of Chebyshev’s Inequality complement one another, so that they both can be formulated in a pairing form, including a second inequality, that provides an estimate for the classical one. 1. Introduction The well known fact that the derivative and the integral are inverse each other has a lot of interesting consequences, on...

refined analytical collapse capacity spectra

recently, two of the authors have introduced the collapse capacity spectrummethodology, which allows the assessment of the collapse capacity of highly inelastic p-deltasensitive regular frame structures without performing non-linear time-history analyses. the mainingredient of this method is the collapse capacity spectrum, which represents the seismic collapsecapacity of an inelastic non-deteri...

On the Refined Heisenberg-weyl Type Inequality

The well-known second moment Heisenberg-Weyl inequality (or uncertainty relation) states: Assume that f : R → C is a complex valued function of a random real variable x such that f ∈ L(R), where R = (−∞,∞). Then the product of the second moment of the random real x for |f | and the second moment of the random real ξ for ∣∣∣f̂ ∣∣∣2 is at least ER,|f |2 / 4π, where f̂ is the Fourier transform of f ...

An Operator Extension of Bohr's inequality