Daniele Puglisi

Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras

We study holomorphic maps between C-algebras and , when is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball . If we assume that is orthogonality preserving and orthogonally additive on and contains an invertible element in , then there exist a sequence in and Jordan -homomorphisms such that uniformly in . When is abelian, the hypothesis of being unital and can be relaxed to get the same statement.

Non-Convex Strong Duality Via Subdifferential

In this article, the strong duality is treated. It is shown that the strong duality is equivalent to the non-emptiness of the subdifferential of a sort map involving the constraint functions. It is also noted that this technique is useful to verify the Assumption S. Indeed, the linearity of a constraint function h is not required as usually seen in the literature. Moreover, it is shown that this condition is easer to verify in the applications. We apply this new principle to the bi-obstacle problem, to the elastic-plastic torsion problem and to the continuum model of transportation.

On the Range of a Vector Measure

Let C be a countable subset of co that lies in the range of a (c 0)**-valued measure, then C lies in the range of a co-valued measure. We extend this result to C(K), where K is a compact Hausdorff space, i.e., we let C be a countable subset of C(K) that lies in the range of a C(K)**-valued measure, then C lies in the range of a C(K)-valued measure. We will also see that in any separable Banach space the result still holds

FREMLIN TENSOR PRODUCTS OF BANACH LATTICES

We prove that the Fremlin tensor product of two Banach lattices with the Radon-Nikodym property, with one of them atomic, has the Radon-Nikodym property.

Operators on Bourgain–Delbaen spaces

We prove that, for a suitable choice of real numbers

On i -operators on real normed spaces

a, b

STABILITY ON LOCAL UNCONDITIONAL STRUCTURE AND THE GORDON-LEWIS PROPERTY IN TENSOR PRODUCTS

, every operator from

Lineability in subsets of measure and function spaces

\ell_2

Bounded linear non-absolutely summing operators

to

Positive solutions of quasi-linear elliptic equations with dependence on the gradient

X_{a,b}