Are continuous mappings preserving normality necessarily linear?

Sequentially Continuous Linear Mappings in Constructive Analysis

On Invertibility Preserving Linear Mappings, Simultaneous Triangularization and Property L

1. Introduction. The investigation leading to this publication was motivated by a desire to try to understand the structure of a linear unital mapping ϕ from a unital algebra A of matrices contained in M h (C) into M n (C) which has the property that an invertible element in A is mapped into an invertible in M n (C). The interest in this question was raised by some earlier results on a linear i...

Cdmtcs Research Report Series Sequentially Continuous Linear Mappings in Constructive Analysis Sequentially Continuous Linear Mappings in Constructive Analysis

- Inner Product Preserving Mappings

A mapping f : M → N between Hilbert C∗-modules approximately preserves the inner product if ‖〈f(x), f(y)〉 − 〈x, y〉‖ ≤ φ(x, y), for an appropriate control function φ(x, y) and all x, y ∈ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert C∗modules on more general restricted domains. In particular, we investigate some asympt...

Unit-circle-preserving mappings

If f is an isometry, then every distance r > 0 is conserved by f , and vice versa. We can now raise a question whether each mapping that preserves certain distances is an isometry. Indeed, Aleksandrov [1] had raised a question whether a mapping f : X → X preserving a distance r > 0 is an isometry, which is now known to us as the Aleksandrov problem. Without loss of generality, we may assume r =...