ORTHOGONALITY AND LINEAR MAPPINGS IN BANACH MODULES

Orthogonality preserving mappings on inner product C* -modules

Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping

Linear Orthogonality Preservers of Hilbert C∗-modules

We show in this paper that the module structure and the orthogonality structure of a Hilbert C∗-module determine its inner product structure. Let A be a C∗-algebra, and E and F be Hilbert A-modules. Assume Φ : E → F is an A-module map satisfying 〈Φ(x),Φ(y)〉A = 0 whenever 〈x, y〉A = 0. Then Φ is automatically bounded. In case Φ is bijective, E is isomorphic to F . More precisely, let JE be the cl...

Linear Orthogonality Preservers of Hilbert Modules

We verify in this paper that the linearity and orthogonality structures of a (not necessarily local trivial) Hilbert bundle over a locally compact Hausdorff space Ω determine its unitary structure. In fact, as Hilbert bundles over Ω are exactly Hilbert C0(Ω)-modules, we have a more general set up. A C-linear map θ (not assumed to be bounded) between two Hilbert C∗-modules is said to be “orthogo...

cauchy-rassias stability of linear mappings in banach modules associated with a generalized jensen type mapping