UID:
almahu_9947368111202882
Format:
1 online resource (157 p.)
ISBN:
1-281-77759-5
,
9786611777593
,
0-08-087137-2
Series Statement:
North-Holland mathematics studies ; 26
Content:
Bornologies and functional analysis
Note:
Includes index.
,
Front Cover; Bornologies and Functional Analysis; Copyright Page; CONTENTS; Introduction; CHAPTER 0. PRELIMINARY NOTIONS OF ALGEBRA AND TOPOLOGY; 0.A Vector Spaces; 0.B Preliminaries of General Topology and Normed Spaces; 0.C Topological Vector Spaces; CHAPTER I. BORNOLOGY; 1:1 Definitions; 1:2 Bounded Linear Maps; 1:3 Fundamental Examples of Bornologies; 1:4 Bornological Convergence; CHAPTER II. FUNDAMENTAL BORNOLOGICAL CONSTRUCTIONS; 2:1 Initial Bornologies; 2:2 Product Bornologies; 2:3 Induced Bornologies: Bornological Subspaces; 2:4 Bornologies Generated by a Family of Subsets
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2:5 Bornological Projective Limits2:6 Final Bornologies; 2:7 Quotient Bornologies; 2:8 Bornological Inductive Limits; 2:9 Bornological Direct Sums: Finite-Dimensional Bornologies; 2:10 Stability of the Separation Property; 2:11 Bornologically Closed Sets: Separation of Bornological Quotients; 2:12 The Associated Separated Bornological Vector Space; 2:13 The Structure of a Convex Bornological Space: Comparison with the Structure of a Locally Convex Space; CHAPTER III. COMPLETE BORNOLOGIES; 3:1 Completant Bounded Disks; 3:2 Complete Convex Bornological Spaces
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3:3 Separated Bornological Vector Spaces of Finite Dimension3:4 The Complete Bornology Associated with a Separated Vector Bornology; 3:5 Bornologically Complete Topological Vector Spaces; CHAPTER IV. ""TOPOLOGY -BORNOLOGY"": INTERNAL DUALITY; 4:1 Compatible Topologies and Bornologies]; 4:2 Characterisation of Bornological Topologies; 4:3 Completely Bornological Spaces; 4:4 The Closed Graph Theorem; CHAPTER V. ""TOPOLOGY -BORNOLOGY"": EXTERNAL DUALITY I: THE FUNDAMENTAL PRINCIPLES OF DUALITY; 5:0 Preliminaries: The Hahn-Banach Theorem and its Consequences
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5:1 The External Duality Between Topology and Bornology5:2 Duality Between Equicontinuous and Equibounded Sets in a Dual Space; 5:3 Completeness of the Equicontinuous Bornology: Completely Bornological Topology on A Dual Space; 5:4 Completeness of the Natural Topology on A Bornological Dual; 5:5 External Duality Between Bounded and Continuous Linear Maps : Dual Maps; CHAPTER VI. ""TOPOLOGY - BORNOLOGY"": EXTERNAL DUALITY II: WEAKLY COMPACT BORNOLOGIES AND REFLEXIVITY; 6:1 Weak Compactness of Equicontinuous Sets; 6:2 The Bornology of Weakly Compact Disks and the Mackey-Arens Theorem
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6:3 Weakly Compact Bornologies: Reflexivity6:4 Completely Reflexive Locally Convex Spaces; CHAPTER VII. COMPACT BORNOLOGIES; 7:1 Hypo-Montel Spaces; 7:2 Schwartz spaces; 7:3 Silva Spaces; CHAPTER VIII. DISTRIBUTIONS AND DIFFERENTIAL OPERATORS; 8:0 Multi-Dimensional Notation; 8:1 The Bornological Spaces E(o) and D(o); 8:2 Distributions as Bounded Linear Functionals; 8:3 Differential Operators and Partial Differential Equations; 8:4 The Silva Space E'(o); 8:5 The Spaces E'(K) and the Bornological Structure of E'(o); 8:6 The General Existence Theorem for Infinitely Differentiable Solutions
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8:7 Proof of the Existence Theorem: Sufficiency
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English
Additional Edition:
ISBN 0-7204-0712-5
Language:
English
