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  • 1
    Online Resource
    Online Resource
    Berlin, Heidelberg :Springer Berlin Heidelberg :
    UID:
    almahu_9947921507902882
    Format: XV, 289 p. , online resource.
    ISBN: 9783540379133
    Series Statement: Lecture Notes in Mathematics, 485
    Note: Support functionals for closed bounded convex subsets of a Banach space -- Convexity and differentiability of norms -- Uniformly convex and uniformly smooth Banach spaces -- The classical renorming theorems -- Weakly compactly generated banach spaces -- The Radon-Nikodým theorem for vector measures.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9783540074021
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    URL: Volltext  (lizenzpflichtig)
    URL: Volltext  (Deutschlandweit zugänglich)
    URL: Cover
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  • 2
    UID:
    b3kat_BV041962657
    Format: 1 Online-Ressource
    ISBN: 9783540083566
    Series Statement: Lecture notes in mathematics 604
    Additional Edition: Erscheint auch als Druckausgabe ISBN 978-3-540-37262-2
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Banach-Raum ; Analytische Funktion ; Analytische Funktion ; Banach-Raum ; Banach-Raum ; Funktionalanalysis ; Konferenzschrift ; Konferenzschrift ; Konferenzschrift
    URL: Volltext  (lizenzpflichtig)
    URL: Volltext  (Deutschlandweit zugänglich)
    URL: Cover
    Author information: Diestel, Joseph 1943-
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  • 3
    Book
    Book
    Providence, RI :American Mathemathical Society,
    UID:
    almahu_BV002252679
    Format: xiii, 322 Seiten.
    ISBN: 0-8218-1515-6 , 978-0-8218-1515-1
    Series Statement: Mathematical surveys and monographs volume 15
    Note: Literaturverzeichnis: Seite 277 - 310
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-1-4704-1242-5
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Vektorwertiges Maß ; Banach-Raum ; Banach-Raum
    Author information: Diestel, Joseph, 1943-,
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  • 4
    Book
    Book
    New York [u.a.] :Springer,
    UID:
    almahu_BV000228687
    Format: XI, 261 S.
    ISBN: 0-387-90859-5 , 3-540-90859-5 , 978-1-4612-9734-5
    Series Statement: Graduate texts in mathematics 92
    Note: Hier auch später erschienene, unveränderte Nachdrucke
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-1-4612-5200-9
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Banach-Raum ; Reihe ; Banach-Raum ; Folge ; Konferenzschrift ; Konferenzschrift
    URL: Cover
    Author information: Diestel, Joseph, 1943-
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  • 5
    Book
    Book
    Providence, Rhode Island :American Mathematical Society,
    UID:
    almafu_BV023338724
    Format: X, 278 Seiten : , Diagramme.
    ISBN: 978-0-8218-4440-3
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-1-4704-2483-1
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Banach-Raum ; Tensorprodukt
    Author information: Diestel, Joseph 1943-
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  • 6
    Book
    Book
    Providence, RI :American Math. Soc.,
    UID:
    almahu_BV041413502
    Format: XIV, 320 S.
    ISBN: 978-1-4704-0935-7
    Series Statement: Graduate studies in mathematics 150
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-1-4704-1411-5
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Invariantes Maß ; Haar-Maß ; Topologische Gruppe
    Author information: Diestel, Joseph, 1943-
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  • 7
    Book
    Book
    Providence, RI :American Math. Soc.,
    UID:
    almafu_BV037307105
    Format: XIII, 322 S.
    Edition: reprint.
    ISBN: 978-0-8218-1515-1 , 0-8218-1515-6
    Series Statement: Mathematical surveys 15
    Note: Literaturverz. S. 277 - 310
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Vektorwertiges Maß ; Banach-Raum ; Banach-Raum ; Vektor-Maß ; Vektor-Maß
    Author information: Diestel, Joseph 1943-
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  • 8
    Online Resource
    Online Resource
    Providence, RI :American Mathematical Society,
    UID:
    almahu_BV046430334
    Format: 1 Online-Ressource (xiv, 320 Seiten).
    ISBN: 978-1-4704-1411-5
    Series Statement: Graduate studies in mathematics volume 150
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-1-4704-0935-7
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Invariantes Maß ; Haar-Maß ; Topologische Gruppe
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Diestel, Joseph, 1943-,
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  • 9
    Online Resource
    Online Resource
    Providence, Rhode Island :American Mathematical Society,
    UID:
    almahu_BV043983124
    Format: 1 Online-Ressource (xiii, 322 Seiten).
    ISBN: 978-1-4704-1242-5
    Series Statement: Mathematical surveys and monographs Volume 15
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 0-8218-1515-6
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-0-8218-1515-1
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Vektorwertiges Maß ; Banach-Raum ; Vektorwertiges Maß ; Banach-Raum
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Diestel, Joseph, 1943-,
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  • 10
    Online Resource
    Online Resource
    New York, NY :Springer New York,
    UID:
    almahu_9947362980802882
    Format: XII, 263 p. , online resource.
    ISBN: 9781461252009
    Series Statement: Graduate Texts in Mathematics, 92
    Content: This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac­ titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.
    Note: I. Riesz’s Lemma and Compactness in Banach Spaces. Isomorphic classification of finite dimensional Banach spaces … Riesz’s lemma … finite dimensionality and compactness of balls … exercises … Kottman’s separation theorem … notes and remarks … bibliography. -- II. The Weak and Weak* Topologies: an Introduction. Definition of weak topology … non-metrizability of weak topology in infinite dimensional Banach spaces … Mazur’s theorem on closure of convex sets … weakly continuous functional coincide with norm continuous functionals … the weak* topology … Goldstine’s theorem … Alaoglu’s theorem … exercises … notes and remarks … bibliography. -- III. The Eberlein-Šmulian Theorem. Weak compactness of closed unit ball is equivalent to reflexivity … the Eberlein-Šmulian theorem … exercises … notes and remarks … bibliography. -- IV. The Orlicz-Pettis Theorem. Pettis’s measurability theorem … the Bochner integral … the equivalence of weak subseries convergence with norm subseries convergence … exercises … notes and remarks … bibliography. -- V. Basic Sequences. Definition of Schauder basis … basic sequences … criteria for basic sequences … Mazur’s technique for constructing basic sequences … Pelczynski’s proof of the Eberlein-Šmulian theorem … the Bessaga-Pelczynski selection principle… Banach spaces containing co … weakly unconditionally Cauchy series … co in dual spaces … basic sequences spanning complemented subspaces … exercises … notes and remarks … bibliography. -- VI. The Dvoretsky-Rogers Theorem. Absolutely P-summing operators … the Grothendieck-Pietsch domination theorem … the Dvoretsky-Rogers theorem … exercises … notes and remarks … bibliography. -- VII. The Classical Banach Spaces. Weak and pointwise convergence of se-quences in C(?) … Grothendieck’s characterization of weak convergence … Baire’s characterization of functions of the first Baire class … special features of co, l1l? … injectivity of l? … separable injectivity of co … projectivity of l1 … l1 is primary … Pelczynski’s decomposition method … the dual of l? … the Nikodym-Grothendieck boundedness theorem … Rosenthal’s lemma … Phillips’s lemma … Schur’s theorem … the Orlicz-Pettis theorem (again)… weak compactness in ca(?) and L1 (?) … the Vitali-Hahn-Saks theorem … the Dunford-Pettis theorem … weak sequential completeness of ca(?) and L1(?) … the Kadec-Pelczynski theorem … the Grothendieck-Dieudonne weak compactness criteria in rca … weak* convergent sequences in l?* are weakly convergent … Khintchine’s Inequalities … Orlicz’s theorem … unconditionally convergent series in Lp[0, 1], 1 ? p ? 2 … the Banach-Saks theorem … Szlenk’s theorem … weakly null sequences in Lp [0, 1], 1 ? p ? 2, have subsequences with norm convergent arithmetic means … exercises … notes and remarks … bibliography. -- VIII. Weak Convergence and Unconditionally Convergent Series in Uniformly Convex Spaces. Modulus of convexity … monotonicity and convexity properties of modulus … Kadec’s theorem on unconditionally convergent series in uniformly convex spaces … the Milman-Pettis theorem on reflexivity of uniformly convex spaces … Kakutani’s proof that uniformly convex spaces have the Banach-Saks property … the Gurarii-Gurarii theorem on lp estimates for basic sequences in uniformly convex spaces … exercises … notes and remarks … bibliography. -- IX. Extremal Tests for Weak Convergence of Sequences and Series. The Krein-Milman theorem … integral representations … Bauer’s characterization of extreme points … Milman’s converse to the Krein-Milman theorem … the Choquet integral representation theorem … Rainwater’s theorem … the Super lemma … Namioka’s density theorems … points of weak*-norm continuity of identity map … the Bessaga-Pelczynski characterization of separable duals … Haydon’s separable generation theorem … the remarkable renorming procedure of Fonf … Elton’s extremal characterization of spaces without co-subspaces … exercises … notes and remarks … bibliography. -- X. Grothendieck’s Inequality and the Grothendieck-Lindenstrauss-Pelczynski Cycle of Ideas. Rietz’s proof of Grothendieck’s inequality … definition of ?p spaces … every operator from a ?1-space to a ?2-space is absolutely 1-summing … every operator from a L? space to ?1 space is absolutely 2-summing … c0, l1 and l2 have unique unconditional bases … exercises … notes and remarks … bibliography. -- An Intermission: Ramsey’s Theorem. Mathematical sociology … completely Ramsey sets … Nash-Williams’ theorem … the Galvin-Prikry theorem … sets with the Baire property … notes and remarks … bibliography. -- XI. Rosenthal’s l1-theorem. Rademacher-like systems … trees … Rosenthal’s I1-theorem … exercises … notes and remarks … bibliography. -- XII. The Josefson-Nissenzweig Theorem. Conditions insuring l1’s presence in a space given its presence in the dual … existence of weak* null sequences of norm-one functionals … exercises … notes and remarks … bibliography. -- XIII. Banach Spaces with Weak*-Sequentially Compact Dual Balls. Separable Banach spaces have weak* sequentially compact dual balls … stability results … Grothendieck’s approximation criteria for relative weak compactness … the Davis-Figiel-Johnson-Pelczynski scheme … Amir-Lindenstrauss theorem … subspaces of weakly compactly generated spaces have weak* sequentially compact dual balls … so do spaces each of whose separable subspaces have a separable dual, thanks to Hagler and Johnson … the Odell-Rosenthal characterization of separable spaces with weak* sequentially compact second dual balls … exercises … notes and remarks … bibliography. -- XIV. The Elton-Odell (l + ?)Separation Theorem. James’s co-distortion theorem … Johnson’s combinatorial designs for detecting co’s presence … the Elton-Odell proof that each infinite dimensional Banach space contains a (l + ?)-separated sequence of norm-one elements … exercises … notes and remarks . . bibliography.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781461297345
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Konferenzschrift
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