Positivity, ( ISI ), Volume (21), No (3), Year (2016-9) , Pages (1161-1172)

Title : ( Conditionally positive definite kernels in Hilbert $C^*$-modules )

Authors: Mohammad Sal Moslehian ,

Access to full-text not allowed by authors

Citation: BibTeX | EndNote

Abstract

We investigate the notion of conditionally positive definite in the context of Hilbert $C^*$-modules and present a characterization of the conditionally positive definiteness in terms of the usual positive definiteness. We give a Kolmogorov type representation of conditionally positive definite kernels in Hilbert $C^*$-modules. As a consequence, we show that a $C^*$-metric space $(S, d)$ is $C^*$-isometric to a subset of a Hilbert $C^*$-module if and only if $K(s,t)=-d(s,t)^2$ is a conditionally positive definite kernel. We also present a characterization of the order $K'\leq K$ between conditionally positive definite kernels.

Keywords

, Conditionally positive definite kernel; positive definite kernel; Hilbert $C^*$, module; Kolmogorov respresentation
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

@article{paperid:1059956,
author = {Sal Moslehian, Mohammad},
title = {Conditionally positive definite kernels in Hilbert $C^*$-modules},
journal = {Positivity},
year = {2016},
volume = {21},
number = {3},
month = {September},
issn = {1385-1292},
pages = {1161--1172},
numpages = {11},
keywords = {Conditionally positive definite kernel; positive definite kernel; Hilbert $C^*$-module; Kolmogorov respresentation},
}

[Download]

%0 Journal Article
%T Conditionally positive definite kernels in Hilbert $C^*$-modules
%A Sal Moslehian, Mohammad
%J Positivity
%@ 1385-1292
%D 2016

[Download]