MULTIPLIER SPACES AND THE SUMMING OPERATOR FOR SERIES

作者：Swartz Charles^*

来源：Mathematica Slovaca, 2016, 66(3): 687-694.

DOI：10.1515/ms-2015-0170

• multiplier space
• summing operator
• (weak) compactness
• series
• convergence
• weak sequential continuity
• complete continuity

If {x(j)} is a sequence in a normed space X, the space of bounded multipliers for the series Sigma(j) x(j) is defined to be M-infinity (Sigma x(j)) = {{t(j)} is an element of l(infinity) : Sigma(infinity)(j=1) t(j)x(j) converges} and the summing operator S : M-infinity (Sigma x(j)) -> X is defined to be S({t(j)}) = Sigma(infinity)(j=1) t(j)x(j) . We show that if X is complete, the series Sigma(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.

• 出版日期2016-6