We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X,d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.
In our note, we prove the result that the Hilbert’s cube equipped with metrics, , cannot be isometrically embedded into .
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let be a Hilbert space and let be a positive bounded operator on . The semi-inner product , , induces a semi-norm . This makes into a semi-Hilbertian space. An operator is said to be --normal if for some positive integers and .
In this paper, we give characterizations of certain weak-open images of metric spaces.