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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Representation theorems for unconditionally converging operators


Authors: Joe Howard and Kenneth Melendez
Journal: Proc. Amer. Math. Soc. 45 (1974), 405-408
MSC: Primary 47B37; Secondary 46B05
DOI: https://doi.org/10.1090/S0002-9939-1974-0350488-4
MathSciNet review: 0350488
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Abstract: Let $ N(X)$ be the set $ \{ F\varepsilon X''$: there exists a weakly unconditionally converging series $ \Sigma {x_n}$ in $ X$ such that $ F = \sigma (X'',X') - {\lim _n}\Sigma _{i = 1}^nJ{x_i}\} $. Representation theorems for the unconditionally converging operators (map weakly unconditionally converging series into unconditionally converging series) are developed by using the $ \sigma (X',N(X))$ topology of $ X'$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0350488-4
Keywords: Operator representations, unconditionally converging operator, unconditionally converging series
Article copyright: © Copyright 1974 American Mathematical Society