Ebook: Locally Convex Spaces

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Content:
Front Matter....Pages 1-14
Vector Spaces....Pages 15-29
Topological Vector Spaces....Pages 30-55
Completeness....Pages 56-73
Inductive Linear Topologies....Pages 74-86
Baire Tvs and Webbed Tvs....Pages 87-100
Locally r-Convex Tvs....Pages 101-124
Theorems of Hahn-Banach, Krein-Milman, and Riesz....Pages 125-144
Basic Duality Theory....Pages 145-173
Continuous Convergence and Related Topologies....Pages 174-194
Local Convergence and Schwartz Spaces....Pages 195-218
Barrelledness and Reflexivity....Pages 219-248
Sequential Barrelledness....Pages 249-270
Bornological and Ultrabornological Spaces....Pages 271-288
On Topological Bases....Pages 289-321
The Projective Tensor Product....Pages 323-342
The Injective Tensor Product....Pages 343-367
Some Classes of Operators....Pages 368-396
The Approximation Property....Pages 397-417
Ideals of Operators in Banach Spaces....Pages 418-450
Components of Ideals on Particular Spaces....Pages 451-477
Back Matter....Pages 520-550
Nuclear Locally Convex Spaces....Pages 478-519

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Content:
Front Matter....Pages 1-14
Vector Spaces....Pages 15-29
Topological Vector Spaces....Pages 30-55
Completeness....Pages 56-73
Inductive Linear Topologies....Pages 74-86
Baire Tvs and Webbed Tvs....Pages 87-100
Locally r-Convex Tvs....Pages 101-124
Theorems of Hahn-Banach, Krein-Milman, and Riesz....Pages 125-144
Basic Duality Theory....Pages 145-173
Continuous Convergence and Related Topologies....Pages 174-194
Local Convergence and Schwartz Spaces....Pages 195-218
Barrelledness and Reflexivity....Pages 219-248
Sequential Barrelledness....Pages 249-270
Bornological and Ultrabornological Spaces....Pages 271-288
On Topological Bases....Pages 289-321
The Projective Tensor Product....Pages 323-342
The Injective Tensor Product....Pages 343-367
Some Classes of Operators....Pages 368-396
The Approximation Property....Pages 397-417
Ideals of Operators in Banach Spaces....Pages 418-450
Components of Ideals on Particular Spaces....Pages 451-477
Back Matter....Pages 520-550
Nuclear Locally Convex Spaces....Pages 478-519
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