Taiwanese Journal of Mathematics

UNIFORM CONVERGENCE IN THE DUAL OF A VECTOR-VALUED SEQUENCE SPACE

Charles Swartz and Christopher Stuart

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Abstract

In this note the authors establish several results concerning the uniform convergence of series in vector-valued sequence spaces. Corollaries include sufficient conditions for the weak sequential completeness of β-duals of sequence spaces, versions of the Uniform Boundedness Theorem and the Banach-Steinhaus Theorem for elements of operator-valued β-duals, and a characterization of weakly convergent sequences in β-duals. A further appli- cation establishes a vector-valued version of the Hahn-Schur Lemma.

Article information

Source
Taiwanese J. Math., Volume 7, Number 4 (2003), 665-676.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407585

Digital Object Identifier
doi:10.11650/twjm/1500407585

Mathematical Reviews number (MathSciNet)
MR2017919

Zentralblatt MATH identifier
1044.46007

Citation

Swartz, Charles; Stuart, Christopher. UNIFORM CONVERGENCE IN THE DUAL OF A VECTOR-VALUED SEQUENCE SPACE. Taiwanese J. Math. 7 (2003), no. 4, 665--676. doi:10.11650/twjm/1500407585. https://projecteuclid.org/euclid.twjm/1500407585


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