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Multiplier spaces and the summing operator for series

In: Mathematica Slovaca, vol. 66, no. 3
Charles Swartz
Detaily:
Rok, strany: 2016, 687 - 694
Kľúčové slová:
multiplier space, summing operator, (weak) compactness, series, convergence, weak sequential continuity, complete continuity
O článku:
If $\{x_j\}$ is a sequence in a normed space $X$, the space of bounded multipliers for the series $\sum_j x_j$ is defined to be $M^{\infty}(\sum x_j)=\{\{t_j\}\in l^{\infty}: \sum_{j=1}^{\infty}t_j x_j converges\}$ and the summing operator $S: M^{\infty}(\sum x_j)\to X$ is defined to be $S(\{t_j\})=\sum_{j=1}^{\infty}t_j x_j$. We show that if $X$ is complete, the series $\sum_j x_j$ is subseries convergent iff the operator $S$ is compact and the series is absolutely convergent iff the operator is absolutely summing. Other related results are established.
Ako citovať:
ISO 690:
Swartz, C. 2016. Multiplier spaces and the summing operator for series. In Mathematica Slovaca, vol. 66, no.3, pp. 687-694. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0170

APA:
Swartz, C. (2016). Multiplier spaces and the summing operator for series. Mathematica Slovaca, 66(3), 687-694. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0170
O vydaní:
Publikované: 1. 6. 2016