Currently displaying 1 – 20 of 40

Showing per page

Order by Relevance | Title | Year of publication

Iterated series and the Hellinger-Toeplitz theorem.

Charles Swartz — 1992

Publicacions Matemàtiques

We show that an iterated double series condition due to Antosik implies the uniform convergence of the double series. An application of Antosik's condition is given to the derivation of a vector form of the Hellinger-Toeplitz theorem.

Weak sequential completeness of sequence spaces.

Charles Swartz — 1992

Collectanea Mathematica

Köthe and Toeplitz introduced the theory of sequence spaces and established many of the basic properties of sequence spaces by using methods of classical analysis. Later many of these same properties of sequence spaces were reestablished by using soft proofs of functional analysis. In this note we would like to point out that an improved version of a classical lemma of Schur due to Hahn can be used to give very short proofs of two of the weak sequential completeness results of Köthe and Toeplitz....

Page 1 Next

Download Results (CSV)