We prove that the composition S(u1, . . . , un) of a multilinear multiple 2-summing operator S with 2-summing linear operators uj is nuclear, generalizing a linear result of Grothendieck.

We show that for any operator T : l N ∞ → Y , where Y is a Banach space, that its cotype 2 constant, K (2) (T), is related to its (2, 1)-summing norm, π 2,1 (T), by K (2) (T) ≤ c log log N π 2,1 (T). Thus, we can show that there is an operator T : C(K) → Y that has cotype 2, but is not 2-summing.

We show that the symbol of a bounded composition operator on Wiener algebra Dirichlet series does not need to belong this algebra. Our example even gives an absolutely summing (hence compact) operator.

In this paper we extend the scope of three important results in linear theory absolutely summing operators. The first one was obtained by Bu and Kranz [4] it asserts that a continuous operator between Banach spaces takes almost unconditionally summable sequences into Cohen strongly q-summable for any q≥2, whenever its adjoint is p-summing some p≥1. second them states operators with hilbertian d...

It is shown that the p-summing norm of any operator with n-dimensional domain can be well-aproximated using only " few " vectors in the definition of the p-summing norm. Except for constants independent of n and log n factors, " few " means n if 1 < p < 2 and n p/2 if 2 < p < ∞.

X iv :m at h/ 05 02 30 2v 1 [ m at h. FA ] 1 5 Fe b 20 05 OH-TYPE AND OH-COTYPE OF OPERATOR SPACES AND COMPLETELY SUMMING MAPS HUN HEE LEE Abstract. The definition and basic properties of OH-type and OH-cotype of operator spaces are given. We prove that every bounded linear map from C(K) into OH-cotype q (2 ≤ q < ∞) space (including most of commutative Lq-spaces) for a compact set K satisfies c...

We study when multiplication by a weight can turn non-compact composition operator on \(H^2\) into compact operator, and it be in Schatten classes. The \(q\)-summing case \(H^p\) is considered. also this one.

The interplay between between gauge-field winding numbers, θ-vacua, and the Dirac operator spectrum in finite-volume gauge theories is reconsidered. To assess the weight of each topological sector, we compare the mass-dependent chiral condensate in gauge field sectors of fixed topological index with the answer obtained by summing over the topological charge. Also the microscopic Dirac operator ...

A linear and continuous operator between Banach spaces is said to be absolutely summing if it maps unconditionally convergent series into absolutely convergent series. Moreover, it improves properties of stochastic processes. Indeed, N.Ghoussoub in [7] proved that an operator is absolutely summing if and only if it maps amarts (asymptotic martingales) into uniform amarts. In this paper we go a ...