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.

Abstract Let T: V W be a surjective real linear isometry between full real Hilbert C-modules over real C-algebras A and B, respectively. We show that the following conditions are equivalent:(a) T is a 2-isometry;(b) T is a complete isometry;(c) T preserves ternary products;(d) T preserves inner products;(e) T is a module map. When A and B are commutative, we give a full description of the structure of T.

In this paper, we prove a sum set estimate and the exact sum set theorem for unimodular Kac algebras. Combining the characterization of minimizers of the Donoso–Stark uncertainty principle and the Hirschman–Beckner uncertainty principle, we characterize the extremal pairs of Young’s inequality and extremal operators of the Hausdorff–Young inequality for unimodular Kac algebras.

In this paper we consider the problem of the non-empty intersection of exposed faces in a Banach space. We find a sufficient condition to assure that the non-empty intersection of exposed faces is an exposed face. This condition involves the concept of$inner point$. Finally, we also prove that every minimal face of the unit ball must be an extreme point and show that this is not the case at all for minimal exposed faces since we prove that every Banach space with dimension greater than or equal to 2 can be equivalently renormed to have a non-singleton, minimal exposed face.

In this paper, using the concept of attractive points of a nonlinear mapping, we obtain a strong convergence theorem of Halperns type [<i>Bull. Amer. Math. Soc</i>. <b>73</b> (1967), 957961] for a wide class of nonlinear mappings which contains nonexpansive mappings, nonspreading mappings and hybrid mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems of Halperns type in a Hilbert space. In particular, we solve a problem posed by Kurokawa and Takahashi [<i>Nonlinear Anal</i>. <b>73</b> (2010, 15621568].