Let X and Y be locally compact Hausdorff spaces. We give a full description of disjointness preserving Fredholm linear operators T from C0(X) into C0(Y), and show that is continuous if either Y contains no isolated point or T has closed range. Our task is achieved by writing T as a weighted composition operator Tf = h f . Through the relative homeomorphism , the structure of the range space of T can be completely analyzed, and X and Y are homeomorphic after removing finite subsets.

In this paper we study the distribution of scattering resonances for a multi-dimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.

We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of the continuous section space of a Banach bundle determines completely its bundle structures. We also describe the structure of an into isometry from a continuous section space into an other. However, we demonstrate by an example that a non-surjective linear isometry can be far away from a subbundle embedding.

For Banach lattices X and Y, let X | | Y and X | | Y denote the positive projective and injective tensor products of X and Y, respectively. In this paper, we characterize the inheritance of reflexivity and containment of copies of c 0, 1, by X | | Y and X | | Y from X and Y, when one of them is an atomic Banach lattice. In this case, we also give an affirmative answer to an open question of Jeurnink.

We define type A, type B, type C as well as C*-semi-finite C*-algebras.