Representation theorems for unconditionally converging operators
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- by Joe Howard and Kenneth Melendez PDF
- Proc. Amer. Math. Soc. 45 (1974), 405-408 Request permission
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 $X’$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- 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