Nuclear Locally Convex Spaces / / Albrecht Pietsch.
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| Superior document: | Title is part of eBook package: De Gruyter DGBA Mathematics - <1990 |
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2022] ©1972 |
| Year of Publication: | 2022 |
| Edition: | Translated from the 2nd German Ed. by William H. Ruckle, 1969, Reprint 2021 |
| Language: | English |
| Online Access: | |
| Physical Description: | 1 online resource (204 p.) |
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| LEADER | 06270nam a22006735i 4500 | ||
|---|---|---|---|
| 001 | 9783112564103 | ||
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| 100 | 1 | |a Pietsch, Albrecht, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Nuclear Locally Convex Spaces / |c Albrecht Pietsch. |
| 250 | |a Translated from the 2nd German Ed. by William H. Ruckle, 1969, Reprint 2021 | ||
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2022] | |
| 264 | 4 | |c ©1972 | |
| 300 | |a 1 online resource (204 p.) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Foreword to the First Edition -- |t Foreword to the Second Edition -- |t Contents -- |t Chapter O. Foundations -- |t 0.1. Topological Spaces -- |t 0.2. Metric Spaces -- |t 0.3. Linear Spaces -- |t 0.4. Semi-Norms -- |t 0.5. Locally Convex Spaces -- |t 0.6. The Topological Dual of a Locally Convex Space -- |t 0.7. Special Locally Convex Spaces -- |t 0.8. Banach Spaces -- |t 0.9. Hilbert Spaces -- |t 0.10. Continuous Linear Mappings in Locally Convex Spaces -- |t 0.11. The Normed Spaces Associated 'with a Locally Convex Space -- |t 0.12. Radon Measures -- |t Chapter 1. Summable Families -- |t 1.1. Summable Families of Numbers -- |t 1.2. Weakly Summable Families in Locally Convex Spaces -- |t 1.3. Summable Families in Locally Convex Spaces -- |t 1.4. Absolutely Summable Families in Locally Convex Spaces -- |t 1.5. Totally Summable Families in Locally Convex Spaces -- |t 1.6. Finite Dimensional Families in Locally Convex Spaces -- |t Chapter 2. Absolutely Summing Mappings -- |t 2.1. Absolutely Summing Mappings in Locally Convex Spaces -- |t 2.2. Absolutely Summing Mappings in Normed Spaces -- |t 2.3. A Characterization of Absolutely Summing Mappings in Normed Spaces -- |t 2.4. A Special Absolutely Summing Mappings -- |t 2.5. Hilbert-Schmidt Mappings -- |t Chapter 3. Nuclear Mappings -- |t 3.1. Nuclear Mappings in Normed Spaces -- |t 3.2. Quasinuclear Mappings in Normed Spaces -- |t 3.3. Products of Quasinuclear and Absolutely Summing Mappings in Normed Spaces -- |t 3.4. The Theorem of Dvoretzky and Rogers -- |t Chapter 4. Nuclear Locally Convex Spaces -- |t 4.1. Definition of Nuclear Locally Convex Spaces -- |t 4.2. Summable Families in Nuclear Locally Convex Spaces -- |t 4.3. The Topological Dual of Nuclear Locally Convex Spaces -- |t 4.4. Properties of Nuclear Locally Convex Spaces -- |t Chapter 5. Permanence Properties of Nuclearity -- |t 5.1. Subspaces and Quotient Spaces -- |t 5.2. Topological Products and Sums -- |t 5.3. Complete Hulls -- |t 5.4. Locally Convex Tensor Products -- |t 5.5. Spaces of Continuous Linear Mappings -- |t Chapter 6. Examples of Nuclear Locally Convex Spaces -- |t 6.1. Sequence Spaces -- |t 6.2. Spaces of Infinitely Differentiable Functions -- |t 6.3. Spaces of Harmonic Functions -- |t 6.4. Spaces of Analytic Functions -- |t Chapter 7. Locally Convex Tensor Products -- |t Introduction -- |t 7.1. Definition of Locally Convex Tensor Products -- |t 7.2. Special Locally Convex Tensor Products -- |t 7.3. A Characterization of Nuclear Locally Convex Spaces -- |t 7.4. The Kernel Theorem -- |t 7.5. The Complete π-Tensor Product of Normed Spaces -- |t Chapter 8. Operators of Type l1 and s -- |t 8.1. The Approximation Numbers of Continuous Linear Mappings in Normed Spaces -- |t 8.2. Mappings of Type P -- |t 8.3. The Approximation Numbers of Compact Mappings in Hilbert Spaces -- |t 8.4. Nuclear and Absolutely Summing Mappings -- |t 8.5. Mappings of Type s -- |t 8.6. A Characterization of Nuclear Locally Convex Spaces -- |t Chapter 9. Diametral and Approximative Dimension -- |t 9.1. The Diameter of Bounded Subsets in Normed Spaces -- |t 9.2. The Diametral Dimension of Locally Convex Spaces -- |t 9.3. The Diametral Dimension of Power Series Spaces -- |t 9.4. The Diametral Dimension of Nuclear Locally Convex Spaces -- |t 9.5. A Characterization of Dual Nuclear Locally Convex Spaces -- |t 9.6. The £-Entropy of Bounded Subsets in Normed Spaces -- |t 9.7. The Approximative Dimension of Locally Convex Spaces -- |t 9.8. The Approximative Dimension of Nuclear Locally Convex Spaces -- |t Chapter 10. Nuclear Locally Convex Spaces with Basis -- |t Introduction -- |t 10.1. Locally Convex Spaces with Basis -- |t 10.2. Representation of Nuclear Locally Convex Spaces with Basis -- |t 10.3- Bases in Special Nuclear Localty Convex Spaces -- |t Chapter 11. Universal Nuclear Locally Convex Spaces -- |t 11.1. Imbedding in the Product Space (ξ)1 -- |t 11.2. Embedding in the Product Space (ξ)1 -- |t Bibliography -- |t Index -- |t Table of Symbols |
| 506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
| 530 | |a Issued also in print. | ||
| 538 | |a Mode of access: Internet via World Wide Web. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022) | |
| 650 | 7 | |a MATHEMATICS / Functional Analysis. |2 bisacsh | |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DGBA Mathematics - <1990 |z 9783110635881 |o ZDB-23-GMA |
| 776 | 0 | |c print |z 9783112564097 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9783112564103 |
| 856 | 4 | 0 | |u https://www.degruyter.com/isbn/9783112564103 |
| 856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9783112564103/original |
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