11 papers
Isometries between the unit spheres of spaces of metrics
Katsuhisa Koshino
Given a topological space , let be the space of bounded continuous pseudometrics on , which is endowed with the sup-norm, and let be the unit sphere of $PM(Z…
Banach-Stone type theorems on uniformly continuous and lipschitz continuous pseudometrics
Katsuhisa Koshino
In this paper, we shall establish Banach-Stone type theorems on spaces of uniformly continuous and lipschitz continuous pseudometrics.
Compactness of averaging operators on non-reflexive Lebesgue spaces
Katsuhisa Koshino
Let be a Borel and Borel-regular metric measure space whose closed balls are of positive and finite measure. In this paper, we shall give equivalent conditions for averaging op…
Isometries between spaces of metrics
Katsuhisa Koshino
Given a metrizable space , denote by the space of continuous bounded pseudometrics on , and denote by the one of continuous bounded admissible met…
On isometric universality of spaces of metrics
Yoshito Ishiki, Katsuhisa Koshino
A metric space is said to be universal for a class of metric spaces if all metric spaces in the class can be isometrically embedded into . In this paper, for a met…
On the Borel complexity and the complete metrizability of spaces of metrics
Katsuhisa Koshino
Given a metrizable space , let be the space of continuous bounded admissible metrics on , which is endowed with the sup-metric. In this paper, we shall investigate th…