000			05738nam a22004935i 4500
001			276212
003			IT-RoAPU
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007			cr || ||||||||
008			221201t20221972gw fo d z eng d
019			_a(OCoLC)1302162292
020			_a9783112564097 _qprint
020			_a9783112564103 _qPDF
024	7		_a10.1515/9783112564103 _2doi
035			_a(DE-B1597)9783112564103
035			_a(DE-B1597)607272
035			_a(OCoLC)1301550175
040			_aDE-B1597 _beng _cDE-B1597 _erda
072		7	_aMAT037000 _2bisacsh
084			_aonline - DeGruyter
100	1		_aPietsch, Albrecht _eautore
245	1	0	_aNuclear Locally Convex Spaces / _cAlbrecht Pietsch.
250			_aTranslated from the 2nd German Ed. by William H. Ruckle, 1969, Reprint 2021
264		1	_aBerlin ; _aBoston : _bDe Gruyter, _c[2022]
264		4	_c©1972
300			_a1 online resource (204 p.)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0	0	_tFrontmatter -- _tForeword to the First Edition -- _tForeword to the Second Edition -- _tContents -- _tChapter O. Foundations -- _t0.1. Topological Spaces -- _t0.2. Metric Spaces -- _t0.3. Linear Spaces -- _t0.4. Semi-Norms -- _t0.5. Locally Convex Spaces -- _t0.6. The Topological Dual of a Locally Convex Space -- _t0.7. Special Locally Convex Spaces -- _t0.8. Banach Spaces -- _t0.9. Hilbert Spaces -- _t0.10. Continuous Linear Mappings in Locally Convex Spaces -- _t0.11. The Normed Spaces Associated 'with a Locally Convex Space -- _t0.12. Radon Measures -- _tChapter 1. Summable Families -- _t1.1. Summable Families of Numbers -- _t1.2. Weakly Summable Families in Locally Convex Spaces -- _t1.3. Summable Families in Locally Convex Spaces -- _t1.4. Absolutely Summable Families in Locally Convex Spaces -- _t1.5. Totally Summable Families in Locally Convex Spaces -- _t1.6. Finite Dimensional Families in Locally Convex Spaces -- _tChapter 2. Absolutely Summing Mappings -- _t2.1. Absolutely Summing Mappings in Locally Convex Spaces -- _t2.2. Absolutely Summing Mappings in Normed Spaces -- _t2.3. A Characterization of Absolutely Summing Mappings in Normed Spaces -- _t2.4. A Special Absolutely Summing Mappings -- _t2.5. Hilbert-Schmidt Mappings -- _tChapter 3. Nuclear Mappings -- _t3.1. Nuclear Mappings in Normed Spaces -- _t3.2. Quasinuclear Mappings in Normed Spaces -- _t3.3. Products of Quasinuclear and Absolutely Summing Mappings in Normed Spaces -- _t3.4. The Theorem of Dvoretzky and Rogers -- _tChapter 4. Nuclear Locally Convex Spaces -- _t4.1. Definition of Nuclear Locally Convex Spaces -- _t4.2. Summable Families in Nuclear Locally Convex Spaces -- _t4.3. The Topological Dual of Nuclear Locally Convex Spaces -- _t4.4. Properties of Nuclear Locally Convex Spaces -- _tChapter 5. Permanence Properties of Nuclearity -- _t5.1. Subspaces and Quotient Spaces -- _t5.2. Topological Products and Sums -- _t5.3. Complete Hulls -- _t5.4. Locally Convex Tensor Products -- _t5.5. Spaces of Continuous Linear Mappings -- _tChapter 6. Examples of Nuclear Locally Convex Spaces -- _t6.1. Sequence Spaces -- _t6.2. Spaces of Infinitely Differentiable Functions -- _t6.3. Spaces of Harmonic Functions -- _t6.4. Spaces of Analytic Functions -- _tChapter 7. Locally Convex Tensor Products -- _tIntroduction -- _t7.1. Definition of Locally Convex Tensor Products -- _t7.2. Special Locally Convex Tensor Products -- _t7.3. A Characterization of Nuclear Locally Convex Spaces -- _t7.4. The Kernel Theorem -- _t7.5. The Complete π-Tensor Product of Normed Spaces -- _tChapter 8. Operators of Type l1 and s -- _t8.1. The Approximation Numbers of Continuous Linear Mappings in Normed Spaces -- _t8.2. Mappings of Type P -- _t8.3. The Approximation Numbers of Compact Mappings in Hilbert Spaces -- _t8.4. Nuclear and Absolutely Summing Mappings -- _t8.5. Mappings of Type s -- _t8.6. A Characterization of Nuclear Locally Convex Spaces -- _tChapter 9. Diametral and Approximative Dimension -- _t9.1. The Diameter of Bounded Subsets in Normed Spaces -- _t9.2. The Diametral Dimension of Locally Convex Spaces -- _t9.3. The Diametral Dimension of Power Series Spaces -- _t9.4. The Diametral Dimension of Nuclear Locally Convex Spaces -- _t9.5. A Characterization of Dual Nuclear Locally Convex Spaces -- _t9.6. The £-Entropy of Bounded Subsets in Normed Spaces -- _t9.7. The Approximative Dimension of Locally Convex Spaces -- _t9.8. The Approximative Dimension of Nuclear Locally Convex Spaces -- _tChapter 10. Nuclear Locally Convex Spaces with Basis -- _tIntroduction -- _t10.1. Locally Convex Spaces with Basis -- _t10.2. Representation of Nuclear Locally Convex Spaces with Basis -- _t10.3- Bases in Special Nuclear Localty Convex Spaces -- _tChapter 11. Universal Nuclear Locally Convex Spaces -- _t11.1. Imbedding in the Product Space (ξ)1 -- _t11.2. Embedding in the Product Space (ξ)1 -- _tBibliography -- _tIndex -- _tTable of Symbols
506	0		_arestricted access _uhttp://purl.org/coar/access_right/c_16ec _fonline access with authorization _2star
530			_aIssued also in print.
538			_aMode of access: Internet via World Wide Web.
546			_aIn English.
588	0		_aDescription based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022)
650		7	_aMATHEMATICS / Functional Analysis. _2bisacsh
850			_aIT-RoAPU
856	4	0	_uhttps://doi.org/10.1515/9783112564103
856	4	0	_uhttps://www.degruyter.com/isbn/9783112564103
856	4	2	_3Cover _uhttps://www.degruyter.com/document/cover/isbn/9783112564103/original
942			_cEB
999			_c276212 _d276212