Let A be a C∗-algebra. We prove that every absolutely summing operator from A into l2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite dimensional examples that show that one can not replace the 4-Schatten-von Neumann class by p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of cap...

Central to the theory of free probability is the notion of summing multiplicative functionals on the lattice of non-crossing partitions. In this paper, a graph-theoretic perspective of partitions is investigated in which independent sets in graphs correspond to non-crossing partitions. By associating particular graphs with elements of “zeon” algebras (commutative subalgebras of fermion algebras...

An operator T : E → X between a Banach lattice E and a Banach space X is called b-weakly compact if T (B) is relatively weakly compact for each b-bounded set B in E. We characterize b-weakly compact operators among o-weakly compact operators. We show summing operators are b-weakly compact and discuss relation between Dunford–Pettis and b-weakly compact operators. We give necessary conditions fo...

Let E be a Banach space that does not contain any copy of l and A be a non commutative C∗-algebra. We prove that every absolutely summing operator from A into E∗ is compact, thus answering a question of Pe lczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additiveA∗-valued measure with bounded variation and...