2013/09/21 by T. Oikhberg, Oikhberg, T., E. Spinu +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1309.5434
arxiv created 2013/09/21 · arxiv updated 2013/09/24
Suppose X and Y are Banach spaces, and I, J are operator ideals (for instance, the ideals of strictly singular, weakly compact, or compact operators). Under what conditions does the inclusion I(X,Y) ⊂ J(X,Y), or the equality I(X,Y) = J(X,Y), hold? We examine this question when I, J are the ideals of Dunford-Pettis, strictly (co)singular, finitely strictly singular, inessential, or (weakly) compact operators, while X and Y are non-commutative function spaces. Since such spaces are ordered, we also address the same questions for positive parts of such ideals.