• Corpus ID: 11648122

Notes on topological vector spaces

@article{Semmes2003NotesOT,
  title={Notes on topological vector spaces},
  author={S. Semmes},
  journal={arXiv: Classical Analysis and ODEs},
  year={2003}
}
  • S. Semmes
  • Published 2 April 2003
  • Mathematics, Physics
  • arXiv: Classical Analysis and ODEs
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. 
Notes on algebras and vector spaces of functions
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so
ON LOCALLY HILBERT SPACES
This is an investigation of some basic properties of strictly inductive limits of Hilbert spaces, called locally Hilbert spaces, with respect to their topological properties, the geometry of their
A note on topological direct sum of subspaces
Some properties of topological direct sum of subspaces of a normed space X are discussed. Using the connection between this sum and the decomposition of the identity operator, we consider the
CONTRACTIVE OPERATORS ON TOPOLOGICAL VECTOR SPACES
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
In this paper, we introduce and study the concept of ideal topological vector spaces.
Positivity in Foliated Manifolds and Geometric Applications
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
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
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
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
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.
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
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
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
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
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.
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
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
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
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
...
...