Spaces of Compact Operators.
We give an explicit description of a tensor norm equivalent on to the associated tensor norm to the ideal of -absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to .
Let M and N be nonzero subspaces of a Hilbert space H satisfying M ∩ N = {0} and M ∨ N = H and let T ∈ ℬ(H). Consider the question: If T leaves each of M and N invariant, respectively, intertwines M and N, does T decompose as a sum of two operators with the same property and each of which, in addition, annihilates one of the subspaces? If the angle between M and N is positive the answer is affirmative. If the angle is zero, the answer is still affirmative for finite rank operators but there are...
In this paper it is shown that the class LnWU (E1,E2,...,En;F) of weakly uniformly continuous n-linear mappings from E1x E2x...x En to F on bounded sets coincides with the class LnWSC (E1,E2,...,En;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space Ei for i = 1,2,...,n does not contain a copy of l1.