# Notes on topological vector spaces

@article{Semmes2003NotesOT, title={Notes on topological vector spaces}, author={S. Semmes}, journal={arXiv: Classical Analysis and ODEs}, year={2003} }

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

## 1,547 Citations

Notes on algebras and vector spaces of functions

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CONTRACTIVE OPERATORS ON TOPOLOGICAL VECTOR SPACES

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In this paper we define contractive bounded linear operators on partially ordered Haussdorff topological vector space and study theirs basic properties.

Ideal Topological Vector Spaces

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In this paper, we introduce and study the concept of ideal topological vector spaces.

Positivity in Foliated Manifolds and Geometric Applications

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We introduce the notion of positivity for a real basic (1, 1) class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity and the negativity…

Topological Vector Spaces

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A topological vector space X over \(\mathbb{R}\) or \(\mathbb{C}\) is a vector space, which is also a topological space, in which the vector space operations are continuous.

An introduction to locally convex cones

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- 2017

This survey introduces and motivates the foundations of the theory of locally convex cones which aims to generalize the well-established theory of locally convex topological vector spaces. We explain…

ON LOCALLY BOUNDED SPACES AND THEIR

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- 2005

In this paper we present a new characterization of locally bounded topological vector spaces, which generalize earlier characterizations of Aoki [1] and Rolewicz [13]. Further we shall prove that…

A note on equivalence preserving maps

- MathematicsLinear and Multilinear Algebra
- 2019

ABSTRACT Let be the algebra of all bounded linear operators on complex Banach space and let the relation , , denote B=TAS for some invertible . We will give a complete description of surjective maps…

## References

SHOWING 1-10 OF 43 REFERENCES

Introduction to Fourier Analysis on Euclidean Spaces.

- Mathematics
- 1971

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action…

An F-space sampler

- Mathematics
- 1984

1. Preliminaries 2. Some of the classic results 3. Hardy spaces 4. The Hahn-Banach extension property 5. Three space problems 6. Lifting Theorems 7. Transitive spaces and small operators 8. Operators…

A Primer of Real Analytic Functions

- Mathematics
- 1992

Preface to the Second Edition * Preface to the First Edition * Elementary Properties * Multivariable Calculus of Real Analytic Functions * Classical Topics * Some Questions of Hard Analysis * Results…

Function theory in several complex variables

- Mathematics
- 2001

Fundamental theory: Holomorphic functions and domains of holomorphy Implicit functions and analytic sets The Poincare, Cousin, and Runge problems Pseudoconvex domains and pseudoconcave sets…

Topological Vector Spaces

- Mathematics
- 1967

This chapter presents the most basic results on topological vector spaces. With the exception of the last section, the scalar field over which vector spaces are defined can be an arbitrary,…

Fourier Analysis on Local Fields.

- Mathematics
- 1975

This book presents a development of the basic facts about harmonic analysis on local fields and the "n"-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy…

Hardy spaces on homogeneous groups

- Mathematics
- 1982

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a…

Geometric Nonlinear Functional Analysis

- Mathematics
- 1999

Introduction Retractions, extensions and selections Retractions, extensions and selections (special topics) Fixed points Differentiation of convex functions The Radon-Nikodym property Negligible sets…

Introduction to H[p] spaces

- Mathematics
- 1998

Preface Preface to the first edition 1. Rudiments 2. Theorem of the brothers Reisz. Introduction to the space H1 3. Elementary boundary behaviour theory for analytic functions 4. Application of…