scholarly journals Structure of u- Injective Hull in Ultra-Quasi-Pseudo Metric Space

2017 ◽  
Vol 5 (12) ◽  
Keyword(s):  
Metric Space ◽  
Injective Hull

scholarly journals The ideal of Lipschitz classical p-compact operators and its injective hull

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Toufik Tiaiba ◽  
Dahmane Achour
Keyword(s):  
Banach Space ◽  
Compact Operator ◽  
Metric Space ◽  
Metric Spaces ◽  
Compact Operators ◽  
Operator Ideal ◽  
Linear Case ◽  
Injective Hull ◽  
Nuclear Operators ◽  
The Ideal

Abstract We introduce and investigate the injective hull of the strongly Lipschitz classical p-compact operator ideal defined between a pointed metric space and a Banach space. As an application we extend some characterizations of the injective hull of the strongly Lipschitz classical p-compact from the linear case to the Lipschitz case. Also, we introduce the ideal of Lipschitz unconditionally quasi p-nuclear operators between pointed metric spaces and show that it coincides with the Lipschitz injective hull of the ideal of Lipschitz classical p-compact operators.

The Ultra-Quasi-Metrically Injective Hull of a T 0-Ultra-Quasi-Metric Space

2012 ◽  
Vol 21 (6) ◽  
pp. 651-670 ◽  
Author(s):  
Hans-Peter A. Künzi ◽  
Olivier Olela Otafudu
Keyword(s):  
Metric Space ◽  
Injective Hull

scholarly journals Ultra-Quasi-Metrically Tight Extensions of Ultra-Quasi-Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Collins Amburo Agyingi
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Injective Hull ◽  
Similar Construction ◽  
Nonexpansive Maps

The concept of the tight extension of a metric space was introduced and studied by Dress. It is known that Dress theory is equivalent to the theory of the injective hull of a metric space independently discussed by Isbell some years earlier. Dress showed in particular that for a metric space X the tight extension TX is maximal among the tight extensions of X. In a previous work with P. Haihambo and H.-P. Künzi, we constructed the tight extension of a T0-quasi-metric space. In this paper, we continue these investigations by presenting a similar construction in the category of UQP-metric spaces and nonexpansive maps.

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

Sign in / Sign up

Export Citation Format

Share Document