BANACH IDEALS OF P-COMPACT OPERATORS

The main theme of this paper is a study in some detail of Banach ideals of continuous linear operators between Banach spaces factoring compactly through lp (1≤p<∞) or co, called p-compact and ∞-compact operators respectively. Recently operators of these types have been studied in [4] within the framework of locally convex spaces which are dense subspaces of p-compact projective limits of Banach spaces. These ideals show close resemblance to the ideals of p-nuclear operators-for the case p=∞ they coincide. Analogously to results of Grothendieck concerning continuous linear operators, we consider vector sequence spaces isometric isomorphic to certain spaces of compact linear operators. A representation theorem for p-compact operators is deduced and isometric properties of the ideal norm are treated. The paper also includes some remarks on unconditional convergence and related operator ideals and a representation for the complete e{open}-tensor product {Mathematical expression} (1≤p<∞) is given. © 1979 Springer-Verlag.