Two‐sided estimates and positivity conditions for solutions of linear operator equations in a Banach lattice

Let A and be bounded linear operators in a Banach lattice B, and M be a positive operator in B. The paper deals with the equation where X should be found and are real numbers. Two‐sided estimates and positivity conditions for a solution of that equation are established. The illustrative examples are also presented.     

Powers of positive elements in C*‐algebras

In this paper, we show that Ogasawa’s theorem has a proof in Bishop style constructive mathematics (BISH). In 25 , we introduced the elementary constructive theory of C*‐algebras in BISH, but we did not discuss the powers of positive elements there. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Covering numbers of isotropic reproducing kernels on compact two‐point homogeneous spaces

In this paper we present upper and lower estimates for the covering numbers of the unit ball of a reproducing kernel Hilbert space associated to a continuous isotropic kernel on a compact two‐point homogeneous space (CTPHS). These estimates are obtained from estimates on the decay of the Fourier–Jacobi coefficients of the kernel via applications of the Funk–Hecke formula and the Schoenberg series representation of an isotropic kernel on CTPHS and also by the use of cubature formulas on these spaces.     

Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation,II

This paper is a continuation of our recent paper 8 . We will consider the semi‐linear Cauchy problem for wave models with scale‐invariant time‐dependent mass and dissipation and power non‐linearity. The goal is to study the interplay between the coefficients of the mass and the dissipation term to prove global existence (in time) of small data energy solutions assuming suitable regularity on the L² scale with additional L¹ regularity for the data. In order to deal with this L² regularity in the non‐linear part, we will develop and employ some tools from Harmonic Analysis.     

M‐constants in Orlicz–Lorentz function spaces

In this paper some lower and upper estimates of M‐constants for Orlicz–Lorentz function spaces for both, the Luxemburg and the Amemiya norms, are given. Since degenerated Orlicz functions φ and degenerated weighted sequences ω are also admitted, this investigations concern the most possible wide class of Orlicz–Lorentz function spaces. M‐constants were defined in 1969 by E. A. Lifshits, and used by many authors in the study of lattice structures on Banach spaces, as well as in the fixed point theory.