From Hahn-Banach to monotonicity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | 2., expanded ed. |
| Series: | Lecture notes in mathematics
1693 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 1. Aufl. u.d.T.: Simons, Stephen : Minimax and monotonicity |
| Physical Description: | XIV, 244 S. graph. Darst. |
| ISBN: | 9781402069185 |
Staff View
MARC
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| 100 | 1 | |a Simons, Stephen |d 1938- |e Verfasser |0 (DE-588)120302225 |4 aut | |
| 245 | 1 | 0 | |a From Hahn-Banach to monotonicity |c Stephen Simons |
| 250 | |a 2., expanded ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIV, 244 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1693 | |
| 500 | |a 1. Aufl. u.d.T.: Simons, Stephen : Minimax and monotonicity | ||
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Duality theory (Mathematics) | |
| 650 | 4 | |a Monotone operators | |
| 650 | 4 | |a Monotonic functions | |
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| 650 | 0 | 7 | |a Hahn-Banach-Fortsetzungssatz |0 (DE-588)4158765-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804137308885090304 |
|---|---|
| adam_text | Table
of
Contents
Introduction
.................................................. 1
I The Hahn-Banach-Lagrange theorem and some consequences
1
The
Hahn—Banach—Lagrange
theorem
.................... 15
2
Applications to functional analysis
....................... 23
3
A minimax theorem
...................................... 24
4
The dual and bidual of a normed space
.................. 25
5
Excess, duality gap, and minimax criteria for weak
compactness
.............................................. 28
6
Sharp
Lagrange
multiplier and KKT results
.............. 32
II
Fenchel
duality
7
A sharp version of the
Fenchel
Duality theorem
.......... 41
8 Fenchel
duality with respect to a bilinear form
—
locally convex spaces
..................................... 44
9
Some properties of |||
·
||2
................................ 49
10
The conjugate of a sum in the locally convex case
....... 51
11 Fenchel
duality vs the conjugate of a sum
................ 54
12
The restricted biconjugate and
Fenchel—
Moreau points
... 58
13
Surrounding sets and the
dom
lemma
.................... 60
14
The
θ
-theorem
..........................................
62
15
The Attouch-Brezis theorem
............................ 65
16
A bivariate Attouch-Brezis theorem
..................... 67
XII Table of
Contents
III Multifunctions, SSD
spaces,
monotonicity and Fitzpatrîck
functions
17
Multifunctions, monotonicity and maximality
............ 71
18
Subdifferentials
are maximally
monotone
................ 74
19
SSD
spaces, q—positive sets and
ВС—
functions
............ 79
20
Maximally q—positive sets in SSD spaces
................. 86
21
SSDB spaces
............................................ 88
22
The SSD space
E x E*
................................... 93
23 Fitzpatrick
functions and fitzpatriflcations
............... 99
24
The maximal monotonicity of a sum
..................... 103
IV Monotone multifunctions on general Banach spaces
25
Monotone multifunctions with bounded range
........... 107
26
A general local boundedness theorem
................... 108
27
The six set theorem and the nine set theorem
........... 108
28
D(SV) and various hulls
..................................
Ill
V Monotone multifunctions on reflexive Banach spaces
29
Criteria for maximality, and Rockafellar s surjectivity
theorem
................................................. 117
30
Surjectivity and an abstract Hammerstein theorem
...... 123
31
The Brezis—Haraux condition
............................ 125
32
Bootstrapping the sum theorem
......................... 128
33
The
>
six set and the
>
nine set theorems for pairs
of multifunctions
......................................... 130
34
The Brezis-Crandall-Pazy condition
..................... 132
Table
of Contents
XIII
VI Special
maximally
monotone multifunctions
35
The norm-dual of the
space
Ε χ Ε*
and BC-functions
... 139
36
Subclasses of the maximally monotone multifunctions
... 147
37
First application of Theorem
35.8:
type (D) implies
type (FP)
................................................ 153
38
TccbÌE**), TccbmÌB*)
and type (ED)
..................... 154
39
Second application of Theorem
35.8:
type (ED) implies
type (FPV)
............................................... 157
40
Final applications of Theorem
35.8:
type (ED) implies
strong
.................................................... 158
41
Strong maximality and coercivity
........................ 159
42
Type (ED) implies type (ANA) and type (BR)
........... 161
43
The closure of the range
................................. 167
44
The sum problem and the closure of the domain
......... 170
45
The biconjugate of a maximum and TccB^E**)
............ 172
46
Maximally monotone multifunctions with convex graph
.. 180
47
Possibly discontinuous positive linear operators
......... 183
48
Subtler properties of subdifferentials
.................... 188
49
Saddle functions and type (ED)
......................... 192
VII
The sum problem for general Banach spaces
50
Introductory comments
.................................. 197
51
Voisei s theorem
......................................... 197
52
Sums with normality maps
.............................. 198
53
A theorem of Verona—Verona
............................ 199
XIV Table of
Contents
VIII
Open problems
203
IX Glossary of classes of mult
ifimet
ions
205
X A selection of results
207
References
................................................... 233
Subject index
............................................... 239
Symbol index
............................................... 243
|
| adam_txt |
Table
of
Contents
Introduction
. 1
I The Hahn-Banach-Lagrange theorem and some consequences
1
The
Hahn—Banach—Lagrange
theorem
. 15
2
Applications to functional analysis
. 23
3
A minimax theorem
. 24
4
The dual and bidual of a normed space
. 25
5
Excess, duality gap, and minimax criteria for weak
compactness
. 28
6
Sharp
Lagrange
multiplier and KKT results
. 32
II
Fenchel
duality
7
A sharp version of the
Fenchel
Duality theorem
. 41
8 Fenchel
duality with respect to a bilinear form
—
locally convex spaces
. 44
9
Some properties of |||
·
||2
. 49
10
The conjugate of a sum in the locally convex case
. 51
11 Fenchel
duality vs the conjugate of a sum
. 54
12
The restricted biconjugate and
Fenchel—
Moreau points
. 58
13
Surrounding sets and the
dom
lemma
. 60
14
The
θ
-theorem
.
62
15
The Attouch-Brezis theorem
. 65
16
A bivariate Attouch-Brezis theorem
. 67
XII Table of
Contents
III Multifunctions, SSD
spaces,
monotonicity and Fitzpatrîck
functions
17
Multifunctions, monotonicity and maximality
. 71
18
Subdifferentials
are maximally
monotone
. 74
19
SSD
spaces, q—positive sets and
ВС—
functions
. 79
20
Maximally q—positive sets in SSD spaces
. 86
21
SSDB spaces
. 88
22
The SSD space
E x E*
. 93
23 Fitzpatrick
functions and fitzpatriflcations
. 99
24
The maximal monotonicity of a sum
. 103
IV Monotone multifunctions on general Banach spaces
25
Monotone multifunctions with bounded range
. 107
26
A general local boundedness theorem
. 108
27
The six set theorem and the nine set theorem
. 108
28
D(SV) and various hulls
.
Ill
V Monotone multifunctions on reflexive Banach spaces
29
Criteria for maximality, and Rockafellar's surjectivity
theorem
. 117
30
Surjectivity and an abstract Hammerstein theorem
. 123
31
The Brezis—Haraux condition
. 125
32
Bootstrapping the sum theorem
. 128
33
The
>
six set and the
>
nine set theorems for pairs
of multifunctions
. 130
34
The Brezis-Crandall-Pazy condition
. 132
Table
of Contents
XIII
VI Special
maximally
monotone multifunctions
35
The norm-dual of the
space
Ε χ Ε*
and BC-functions
. 139
36
Subclasses of the maximally monotone multifunctions
. 147
37
First application of Theorem
35.8:
type (D) implies
type (FP)
. 153
38
TccbÌE**), TccbmÌB*)
and type (ED)
. 154
39
Second application of Theorem
35.8:
type (ED) implies
type (FPV)
. 157
40
Final applications of Theorem
35.8:
type (ED) implies
strong
. 158
41
Strong maximality and coercivity
. 159
42
Type (ED) implies type (ANA) and type (BR)
. 161
43
The closure of the range
. 167
44
The sum problem and the closure of the domain
. 170
45
The biconjugate of a maximum and TccB^E**)
. 172
46
Maximally monotone multifunctions with convex graph
. 180
47
Possibly discontinuous positive linear operators
. 183
48
Subtler properties of subdifferentials
. 188
49
Saddle functions and type (ED)
. 192
VII
The sum problem for general Banach spaces
50
Introductory comments
. 197
51
Voisei's theorem
. 197
52
Sums with normality maps
. 198
53
A theorem of Verona—Verona
. 199
XIV Table of
Contents
VIII
Open problems
203
IX Glossary of classes of mult
ifimet
ions
205
X A selection of results
207
References
. 233
Subject index
. 239
Symbol index
. 243 |
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| id | DE-604.BV023067446 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:31:33Z |
| indexdate | 2024-07-09T21:10:14Z |
| institution | BVB |
| isbn | 9781402069185 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016270623 |
| oclc_num | 254627251 |
| open_access_boolean | |
| owner | DE-706 DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-19 DE-BY-UBM DE-188 |
| owner_facet | DE-706 DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-19 DE-BY-UBM DE-188 |
| physical | XIV, 244 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Simons, Stephen 1938- Verfasser (DE-588)120302225 aut From Hahn-Banach to monotonicity Stephen Simons 2., expanded ed. Berlin [u.a.] Springer 2008 XIV, 244 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1693 1. Aufl. u.d.T.: Simons, Stephen : Minimax and monotonicity Banach spaces Duality theory (Mathematics) Monotone operators Monotonic functions Monotone Funktion (DE-588)4294665-7 gnd rswk-swf Multifunktion (DE-588)4434824-1 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 gnd rswk-swf Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 s Konvexe Analysis (DE-588)4138566-4 s Monotone Funktion (DE-588)4294665-7 s Multifunktion (DE-588)4434824-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4020-6919-2 Lecture notes in mathematics 1693 (DE-604)BV000676446 1693 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016270623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simons, Stephen 1938- From Hahn-Banach to monotonicity Lecture notes in mathematics Banach spaces Duality theory (Mathematics) Monotone operators Monotonic functions Monotone Funktion (DE-588)4294665-7 gnd Multifunktion (DE-588)4434824-1 gnd Konvexe Analysis (DE-588)4138566-4 gnd Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 gnd |
| subject_GND | (DE-588)4294665-7 (DE-588)4434824-1 (DE-588)4138566-4 (DE-588)4158765-0 |
| title | From Hahn-Banach to monotonicity |
| title_auth | From Hahn-Banach to monotonicity |
| title_exact_search | From Hahn-Banach to monotonicity |
| title_exact_search_txtP | From Hahn-Banach to monotonicity |
| title_full | From Hahn-Banach to monotonicity Stephen Simons |
| title_fullStr | From Hahn-Banach to monotonicity Stephen Simons |
| title_full_unstemmed | From Hahn-Banach to monotonicity Stephen Simons |
| title_short | From Hahn-Banach to monotonicity |
| title_sort | from hahn banach to monotonicity |
| topic | Banach spaces Duality theory (Mathematics) Monotone operators Monotonic functions Monotone Funktion (DE-588)4294665-7 gnd Multifunktion (DE-588)4434824-1 gnd Konvexe Analysis (DE-588)4138566-4 gnd Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 gnd |
| topic_facet | Banach spaces Duality theory (Mathematics) Monotone operators Monotonic functions Monotone Funktion Multifunktion Konvexe Analysis Hahn-Banach-Fortsetzungssatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016270623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT simonsstephen fromhahnbanachtomonotonicity |