Factorable bounded operators and Schwartz spaces

Abstract

A necessary condition for factoring continuous linear maps with domain co or 1l through a class of spaces which include the 4p spaces (in fact, include the Y, spaces) for 2_p Z and J:Z-* Y such that S=JT. Let en be the sequence with one in the nth place and zero otherwise. A variety (see [2] or [3]) is a collection of locally convex topological vector spaces closed with respect to taking subspaces, quotients by closed subspaces, products and isomorphic images. If B is a locally convex topological vector space, we let v(B) be the Received by the editors March 26, 1973 and, in revised form, April 30, 1973. AMS (MOS) subject classiflcations (1970). Primary 46E30, 46A15; Secondary 47A99, 47B99.