Decomposability of Cylindrical Martingales and Absolutely Summing Operators.
Decomposable subspaces of Banach spaces.
We introduce and study the notion of hereditarily A-indecomposable Banach space for A a space ideal. For a hereditarily A-indecomposable space X we show that the operators from X into a Banach space Y can be written as the union of two sets A Φ+(X,Y) and A(X;Y ). For some ideals A defined in terms of incomparability, the first set is open, the second set correspond to a closed operator ideal and the union is disjoint.
Diagonal and Convolution Operators as Elements of Operator Ideals.
Diagonal mappings between sequence spaces
Diagonal nuclear operators
Diagonal operators on spaces of measurable functions.
Diagonal operators on spaces of measurable functions
Distance between states and statistical inference in quantum theory
Distirbution of eigenvalues and nuclearity
Dominated operators on C[0, 1] and the (CRP).
We show that a B-space E has the (CRP) if and only if any dominated operator T from C[0, 1] into E is compact. Hence we apply this result to prove that c0 embeds isomorphically into the B-space of all compact operators from C[0, 1] into an arbitrary B-space E without the (CRP).
Duality and Lorentz-Marcinkiewicz operator spaces.
Duality between Spaces of p-Summable Sequences (p, g)-Summing Operators and Characterizations of Nuclearity.
Duality of measures of non-𝒜-compactness
Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map (respectively, ) acting on the operators of the surjective (respectively, injective) hull of such that (respectively, ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving and ....
Duals of spaces of compact operators