A note on uniformly dominated sets of summing operators

作者：J M Delgado; C Pi eiro

来源：International Journal of Mathematics and Mathematical Sciences, 2002.

DOI：10.1155/s0161171202007688

Let Y be a Banach space that has no finite cotype and p a real number satisfying 1%26#8804;p%26#60;%26#8734;. We prove that a set %26#8499;%26#8834;%26#928;p(X,Y) is uniformly dominated if and only if there exists a constant C%26#62;0 such that, for every finite set {(xi,Ti):i=1,%26#8230;,n}%26#8834;X%26#215;%26#8499;, there is an operator T%26#8712;%26#928;p(X,Y) satisfying %26#960;p(T)%26#8804;C and %26#8214;Tixi%26#8214;%26#8804;%26#8214;Txi%26#8214; for i=1,%26#8230;,n.

• 出版日期2002