A characterization of compact linear mappings

Operator ideals and spaces of bilinear operators

“…With this theorem we are able to prove the following characterization of compact bilinear operators and this extends a characterization of compact linear operators due to Terzioglu [9]; see also Randtke [6]. THEOREM 2.7 For T E BL(X x Y; Z ) the following are equivalent 1" T is compact 2" There exist continuous bilinear functionals 4, on X x Y with lirnl/4,l/ = 0, such that for all (x, y) E X x Y…”

A note on embedding into product spaces

“…This follows because K is idempotent and has the Hahn-Banach Extension property. The latter statement is a consequence of a well-known theorem of Terzioglu [14] on the characterisation of compact operators on Banach spaces. The above corollary, therefore, yields a simpler and a more general approach to the construction of universal generators for Schwartz spaces.…”

Representation Theorems for Compact Operators

“…Remark. Compact linear operators having representations of the form described in Theorem 3(a) have been studied by Terzioglu [8] and [9], and independently by the author [6]. By using the results of [6] it is easy to see that Theorem 3 remains valid if the hypothesis, that £ be a Fréchet space, is replaced by the weaker hypothesis that £be a sequentially complete locally convex space satisfying any one of the conditions of [6, 2.12].…”