Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

The Karolyhazy uncertainty relation states that if a device is used to measure length l, there will be minimum $$\delta l$$ in the measurement, given by $$(\delta l)^3 \sim L_{\mathrm {P}}^2 . This consequence of combining principles quantum mechanics and general relativity. In this letter we show how arises our approach gravity, bottom-up fashion, from matrix dynamics atoms space–time–matter. ...

A new approach to counterexamples to A new approach to counterexamples to L The derivation of counterexamples to L 1 estimates can be reduced to a geometric decomposition procedure along rank-one lines in matrix space. We illustrate this concept in two concrete applications. Firstly, we recover a celebrated, and rather complex, counterexample by Ornstein, proving the failure of Korn's inequalit...

it is called nontrivial if {0} 6= J 6= X. This notion was introduced by Alfsen and Effros [1] and has proved useful in Banach space geometry, approximation theory and harmonic analysis; see [12] for a detailed account. A number of authors have studied the M -ideal structure in L(X), the space of bounded linear operators on a Banach space X, with special emphasis on the question whether K(X), th...

Truncated Conformal Space Approach (TCSA) is a highly efficient method to compute spectra, operator matrix elements and time evolution in quantum field theories defined as relevant perturbations of 1+1-dimensional conformal theories. However, similarly other exact diagonalisation methods, TCSA ridden with the “curse dimensionality”: dimension Hilbert space increases exponentially (square root t...

Abstract. We study the homogeneous wave equation with radially symmetric data in n ≥ 4 space dimensions. Using some new integral representations for the Riemann operator, we estimate the L∞-norm of the solution. Our results refine those of Kubo [2, 3] in odd space dimensions as well as those of Kubo and Kubota [5] in even space dimensions. However, our approach does not really depend on the par...