‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...

The notion of Lipschitz p-summing operator is introduced. A non linear Pietsch factorization theorem is proved for such operators and it is shown that a Lipschitz p-summing operator that is linear is a p-summing operator in the usual sense.

Let X, Y and Z be Banach spaces, and let ∏ p(Y, Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T : X⊗̂ǫY −→ Z is 1-summing if and only if a naturally associated operator T : X −→ ∏ 1(Y, Z) is 1-summing. This result need not be true if X is not a £∞-space. For p > 1, several examples are given with X = C[0, 1] t...

A Banach space X has the 2-summing property if the norm of every linear operator from X to a Hilbert space is equal to the 2-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar eld: the property is self-dual and any space with the property is a nite dimensional space of maximal distance to the Hilbert space of the same dimensio...

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and l2 is 2-summing. However, it is shown in [7] that the operator space analogue fails. Not every cb-map v : K → OH is completely 2-summing. In this paper, we show an operator space analogue of Maurey’s theorem : Every cb-map v : K → OH is (q, cb)-summing for any q > 2 and hence admits a fact...

A Banach space X has the 2-summing property if the norm of every linear operator from X to a Hilbert space is equal to the 2-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar field: the property is self-dual and any space with the property is a finite dimensional space of maximal distance to the Hilbert space of the same dime...

We prove that a Banach space E has the compact range property (CRP) if and only if for any given C∗-algebra A, every absolutely summing operator from A into E is compact. Related results for p-summing operators (0 < p < 1) are also discussed as well as operators on non-commutative L-spaces and C∗-summing operators.