Esterlè's proof of the tauberian theorem for Beurling algebras

A Tauberian Theorem for Stretchings

R. C. Buck fl] has shown that if a regular matrix sums every subsequence of a sequence x, then x is convergent. I. J. Maddox [4] improved Buck's theorem by showing that if a non-Schur matrix sums every subsequence of a sequence x, then x is convergent. Actually Maddox proved a stronger result: If x is divergent and A sums every subsequence of x, then A is a Schur matrix, i.e., It should be rema...

A New Proof of the Construction Theorem for Stone Algebras

A simple proof is given of Chen's and Grätzer's theorem, which gives a method to construct a Stone algebra from a Boolean algebra and a distributive lattice with 1 by certain connective conditions between the two given lattices. C. C. Chen and G. Grätzer [1] proved originally the Construction Theorem for Stone algebras. In [3] we proved by different method the Construction Theorem for a larger ...

A proof of the Russo–Dye theorem for JB∗-algebras

We give a new and clever proof of the Russo–Dye theorem for JB∗-algebras, which depends on certain recent tools due to the present author. The proof given here is quite different from the known proof by J. D. M. Wright and M. A. Youngson. The approach adapted here is motivated by the corresponding C∗-algebra results due to L. T. Gardner, R. V. Kadison and G. K. Pedersen. Accordingly, it yields ...

The Wiener-Pitt tauberian theorem

An alternative proof of a Tauberian theorem for Abel summability method

Using a corollary to Karamata’s main theorem [Math. Z. 32 (1930), 319—320], we prove that if a slowly decreasing sequence of real numbers is Abel summable, then it is convergent in the ordinary sense. Subjclass [2010] : 40A05; 40E05; 40G10.