Strict convexity and complex strict convexity: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Dekker
1984
|
| Schriftenreihe: | Lecture notes in pure and applied mathematics
89 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 312 S. |
| ISBN: | 0824717961 |
Internformat
MARC
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| 100 | 1 | |a Istrăt̢escu, Vasile I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Strict convexity and complex strict convexity |b theory and applications |
| 264 | 1 | |a New York u.a. |b Dekker |c 1984 | |
| 300 | |a X, 312 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in pure and applied mathematics |v 89 | |
| 650 | 7 | |a Banach, Espaces de |2 ram | |
| 650 | 7 | |a Convexité stricte |2 Jussieu | |
| 650 | 7 | |a Ensembles convexes |2 ram | |
| 650 | 7 | |a Espace Banach complexe |2 Jussieu | |
| 650 | 7 | |a Espace Banach |2 Jussieu | |
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Convex domains | |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Streng konvexer Banach-Raum |0 (DE-588)4183652-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |a Strikte Konvexität |2 gnd |9 rswk-swf | |
| 689 | 0 | 0 | |a Strikte Konvexität |A f |
| 689 | 0 | 1 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
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| 689 | 1 | 0 | |a Streng konvexer Banach-Raum |0 (DE-588)4183652-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in pure and applied mathematics |v 89 |w (DE-604)BV005871364 |9 89 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-000136949 | ||
Datensatz im Suchindex
| _version_ | 1804114691701604352 |
|---|---|
| adam_text | Contents
PREFACE v
1 BANACH SPACES 1
1.1 Linear Spaces 1
1.2 Sets in Linear Spaces 3
1.3 Seminorms and Norms on Linear Spaces.
Locally Convex Spaces 5
1.4 Banach Spaces. Examples 8
1.5 Linear Operators on Banach Spaces.
The Dual Space 10
1.6 Extension Theorems 12
1.7 Three Basic Theorems of Linear Functional
Analysis 17
1.8 Hilbert Spaces 20
2 STRICT CONVEXITY 25
2.1 Strictly Convex Spaces 25
2.2 Product and Quotient Spaces and
Strict Convexity 38
2.3 Interpolation Spaces and Strict Convexity 44
2.4 Uniformly Convex Spaces 52
2.5 Uniform Convexity and Interpolation
Spaces 69
2.6 Some Generalizations of Uniform Convexity 71
2.7 Moduli of Convexity and Smoothness of a
Banach Space 94
2.8 Differentiability Properties of the Norm
and Classes of Banach Spaces 120
2.9 Strictly Convexifiable Spaces.
The Renorming Problem 136
2.10 Strict Convexity and Approximation Theory 181
2.11 Strict Convexity and Fixed Point Theory 188
2.12 Strict Convexity in Probabilistic Metric
Spaces 205
2.13 Extremal Structure in Operator Spaces 210
ix
x Contents
3 COMPLEX STRICT CONVEXITY 241
3.1 Holomorphic Functions with Values in
Banach Spaces 241
3.2 Complex Strictly Convex Spaces 247
3.3 Complex Strictly Convex Spaces and
the Strong Maximum Principle 252
3.4 Products and Quotients of Complex
Strictly Convex Spaces 257
3.5 Complex Uniformly Convex Spaces and
Complex Smooth Convex Spaces 259
3.6 Strongly Complex Extreme Points in Banach
Spaces and Related Classes of Banach Spaces 260
3.7 The Renorming Problem for Complex Strictly
Convex Spaces 264
3.8 Complex Strictly Convex Spaces and
Operator Theory 265
APPENDIX: CLASSES OF OPERATORS AND THE
GEOMETRIC STRUCTURE OF BANACH SPACES 267
A.I Uniformly Convex Operators and
Uniformly Smooth Operators 268
A.2 Uniformly Kadec Klee Operators and
Nearly Uniformly Convex Operators 271
A. 3 Locally Uniformly Convex Operators
and Radon Riesz Operators 273
A.4 Grothendieck Operators 274
A.S k Uniformly Convex Spaces and
k Unjformly Convex Operators 276
A. 6 Final Remarks 279
notation 280
references 282
additional bibliography 305
author index 309
subject index 311
|
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| author | Istrăt̢escu, Vasile I. |
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| ctrlnum | (OCoLC)10230123 (DE-599)BVBBV000228689 |
| dewey-full | 515.7/32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7/32 |
| dewey-search | 515.7/32 |
| dewey-sort | 3515.7 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Strikte Konvexität |
| id | DE-604.BV000228689 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:45Z |
| institution | BVB |
| isbn | 0824717961 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000136949 |
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| physical | X, 312 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Dekker |
| record_format | marc |
| series | Lecture notes in pure and applied mathematics |
| series2 | Lecture notes in pure and applied mathematics |
| spelling | Istrăt̢escu, Vasile I. Verfasser aut Strict convexity and complex strict convexity theory and applications New York u.a. Dekker 1984 X, 312 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in pure and applied mathematics 89 Banach, Espaces de ram Convexité stricte Jussieu Ensembles convexes ram Espace Banach complexe Jussieu Espace Banach Jussieu Banach spaces Convex domains Banach-Raum (DE-588)4004402-6 gnd rswk-swf Streng konvexer Banach-Raum (DE-588)4183652-2 gnd rswk-swf Strikte Konvexität gnd rswk-swf Strikte Konvexität f Banach-Raum (DE-588)4004402-6 s DE-604 Streng konvexer Banach-Raum (DE-588)4183652-2 s Lecture notes in pure and applied mathematics 89 (DE-604)BV005871364 89 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000136949&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Istrăt̢escu, Vasile I. Strict convexity and complex strict convexity theory and applications Lecture notes in pure and applied mathematics Banach, Espaces de ram Convexité stricte Jussieu Ensembles convexes ram Espace Banach complexe Jussieu Espace Banach Jussieu Banach spaces Convex domains Banach-Raum (DE-588)4004402-6 gnd Streng konvexer Banach-Raum (DE-588)4183652-2 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4183652-2 |
| title | Strict convexity and complex strict convexity theory and applications |
| title_auth | Strict convexity and complex strict convexity theory and applications |
| title_exact_search | Strict convexity and complex strict convexity theory and applications |
| title_full | Strict convexity and complex strict convexity theory and applications |
| title_fullStr | Strict convexity and complex strict convexity theory and applications |
| title_full_unstemmed | Strict convexity and complex strict convexity theory and applications |
| title_short | Strict convexity and complex strict convexity |
| title_sort | strict convexity and complex strict convexity theory and applications |
| title_sub | theory and applications |
| topic | Banach, Espaces de ram Convexité stricte Jussieu Ensembles convexes ram Espace Banach complexe Jussieu Espace Banach Jussieu Banach spaces Convex domains Banach-Raum (DE-588)4004402-6 gnd Streng konvexer Banach-Raum (DE-588)4183652-2 gnd |
| topic_facet | Banach, Espaces de Convexité stricte Ensembles convexes Espace Banach complexe Espace Banach Banach spaces Convex domains Banach-Raum Streng konvexer Banach-Raum Strikte Konvexität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000136949&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871364 |
| work_keys_str_mv | AT istratescuvasilei strictconvexityandcomplexstrictconvexitytheoryandapplications |