Topic
Bornological space
About: Bornological space is a research topic. Over the lifetime, 35 publications have been published within this topic receiving 166 citations. The topic is also known as: bornologic space.
Papers
TL;DR: In the context of locally convex spaces, the authors provides an overview of the concepts of holomorphically bornological spaces and Mackey spaces that are more restricted classes than the corresponding linear ones.
Abstract: Publisher Summary This chapter provides an overview of the fact that in the holomorphic approach the corresponding concepts have been introduced as holomorphically bornological, holomorphically barreled, holomorphically infrabaralled, and holomorphically Mackey spaces that are more restricted classes than the corresponding linear ones. In the linear theory of locally convex spaces, it is classical to study bornological, barreled, infrabarreled, and Mackey spaces. An interesting highlight is the holomorphic Banach-Steinhaus on a Frechet space that contains, as a particular case, the classical linear Banach-Steinhaus theorem on such a space. A holomorphically bornological space is also a bornological space. A semimetrizable space is a holomorphically bornological space. A Silva space is known to be essentially the same thing as the dual of a Frechet-Schwartz space, or FS-space; thus, it is also known as a DFS-space. A Silva space is a holomorphically bornological space. Any inductive limit of bornological spaces is a bornological space.
36 citations
TL;DR: In this paper, it was shown that each bounded orthogonally additive homogeneous polynomial acting from an Archimedean vector lattice into a separated convex bornological space can be represented as the composite of a bounded linear operator and a special homogeneous function which plays the role of the exponentiation absent in the lattice.
Abstract: We prove that each bounded orthogonally additive homogeneous polynomial acting from an Archimedean vector lattice into a separated convex bornological space, under the additional assumption that the bornological space is complete or the vector lattice is uniformly complete, can be represented as the composite of a bounded linear operator and a special homogeneous polynomial which plays the role of the exponentiation absent in the vector lattice. The approach suggested is based on the notions of convex bornology and vector lattice power.
28 citations
TL;DR: Quotient spaces are useful as mentioned in this paper and they will be part of functional analysis as soon as functional analysts understand that they are useful and understand how they arrive in spaces with boundedness and then in quotient spaces.
Abstract: Quotient spaces are useful. They will be part of Functional analysis as soon as Functional Analysts understand that they are useful. I have explained how I arrived in spaces with a boundedness, then in quotient spaces.
16 citations
TL;DR: In this article, a general theory for holomorphic functions based on continuous convergence instead of topologies is presented, which can be applied to locally convex spaces and bornological spaces.
Abstract: In this paper we present a general theory for holomorphic functions which is based on continuous convergence instead of topologies. The theory can be applied to locally convex spaces and bornological spaces.
14 citations
13 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 1 |
| 2017 | 1 |
| 2016 | 3 |
| 2014 | 1 |
| 2013 | 2 |