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Publish place: Caspian Journal of Mathematical Sciences، Vol: 3، Issue: 2
Publish Year: 1393
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_CJMS-3-2_010
تاریخ نمایه سازی: 16 مهر 1398
Abstract:
Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous linear operators from $X$ into $Y$. If ${T_{j}}$ is a sequence in $L(X,Y)$, the (bounded) multiplier space for the series $sum T_{j}$ is defined to be [ M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}% T_{j}x_{j}text{ }converges} ] and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associated with the series is defined to be $S({x_{j}})=sum_{j=1}^{infty}T_{j}x_{j}$. In the scalar case the summing operator has been used to characterize completeness, weakly unconditionall Cauchy series, subseries and absolutely convergent series. In this paper some of these results are generalized to the case of operator valued series The corresponding space of weak multipliers is also considered.
Keywords:
multiplier convergent series , multipliers , compact operators , absolutely summing operators , summing operator
Authors
C. Swartz
Mathematics Department, New Mexico State University Las Cruces, NM ۸۸۰۰۳,USA