Geometry of Linear 2-Normed Spaces.

By: Freese, Raymond WContributor(s): Cho, Yeol JePublisher: New York : Nova Science Publishers, Incorporated, 2001Copyright date: ©2005Description: 1 online resource (313 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781621009276Subject(s): Normed linear spacesGenre/Form: Electronic books. Additional physical formats: Print version:: Geometry of Linear 2-Normed SpacesDDC classification: 515/.73 LOC classification: QA322.2 -- .F74 2001ebOnline resources: Click to View
Contents:
Intro -- GEOMETRY OF LINEAR2-NORMED SPACES -- GEOMETRY OF LINEAR2-NORMED SPACES -- CONTENTS -- PREFACE -- CHAPTER 1.INTRODUCTION -- CHAPTER 2.LINEAR 2-NORMED SPACES -- 2.1. Linear Spaces -- 2.2. 2-Norms and 2-Metrics -- 2.3. 2-Norms and Bivectors -- 2.4. Semi-2-Norms and Semi-2-Metrics -- 2.5. 2-Metrics in the Restricted Sense -- 2.6. Between Points and Midpoints -- 2.7. Properties (U) and (L) in Linear 2-Normed Spaces -- 2.8. Properties (U) and (L) in 2-Metric Spaces -- 2.9. Contribution to Non-Archimedean Functional Analysis -- CHAPTER 3.2-BANACH SPACES -- 3.1. Elementary Properties -- 3.2. Bounded Linear 2-Functionals -- 3.3. More Extensions of Bounded Linear 2-Functionals -- CHAPTER 4.COMPLETION OF LINEAR 2-NORMED SPACES -- 4.1. Elementary Properties -- 4.2. Completion of Linear 2-Normed Spaces -- 4.3. Relations between Banach Spaces and 2-Banach Spaces -- CHAPTER 5.2-INNER PRODUCT SPACES -- 5.1. 2-Inner Products -- 5.2. Generating 2-Inner Products -- 5.3. Generalizations of 2-Inner Products -- 5.4. 2-Inner Product Spaces and Gˆateaux Partial Derivatives -- CHAPTER 6.STRICT CONVEXITY -- 6.1. Elementary Characterizations -- 6.2. Strict Convexity by Duality Mappings -- 6.3. Strict Convexity by p-Semi-Inner Products -- 6.4. Strict Convexity by Algebraic and 2-Norm Midpoints -- 6.5. Strict Convexity in Topological Vector Spaces -- 6.6. 2-Norms Generated by Seminorms on the Space ofBivectors -- CHAPTER 7.STRICT 2-CONVEXITY -- 7.1. Elementary Characterizations -- 7.2. Strict 2-Convexity by Algebraic and 2-Norm Midpoints -- 7.3. Strict 2-Convexity by (α, β, γ)-2-Norm Interior Pointsand (α, β, γ)-Algebraic Interior Points -- 7.4. Strict 2-Convexity by Duality Mappings -- 7.5. Strict 2-Convexity by Extreme Points -- CHAPTER 8.UNIFORM CONVEXITY -- 8.1. Elementary Characterizations -- 8.2. Uniform Convexity In Quotient Spaces.
8.3. Uniform Convexity by 2-inner Products -- 8.4. Uniform Convexity by Bivectors -- 8.5. Uniform 2-Convexity in Linear 2-Normed Spaces -- CHAPTER 9.ISOMETRY CONDITIONS IN LINEAR 2-NORMED SPACES -- 9.1. Isometry Conditions -- 9.2. An Example of a Non-linear Isometry -- 9.3. Weak Conditions of Isometries -- 9.4. Non-expansive Mappings in Linear 2-Normed Spaces -- CHAPTER 10.ORTHOGONALITY RELATIONS BETWEENTHE NORMS AND 2-NORMS -- 10.1. Elementary Properties of Orthogonalities -- 10.2. Properties of Orthogonalities and the CharacterizationTheorem -- 10.3. The 2-Dimensional Case and Examples -- 10.4. Orthogonal Triples in Linear 2-Normed Spaces -- CHAPTER 11.QUADRATIC FORMS ON MODULES -- 11.1. Generalized A-Quadratic Forms of Type (P) -- 11.2. Generalized A-Quadratic Forms of Type (Q) -- 11.3. Applications -- 11.4. Extensions to Linear 2-Normed Spaces -- REFERENCES -- INDEX.
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Intro -- GEOMETRY OF LINEAR2-NORMED SPACES -- GEOMETRY OF LINEAR2-NORMED SPACES -- CONTENTS -- PREFACE -- CHAPTER 1.INTRODUCTION -- CHAPTER 2.LINEAR 2-NORMED SPACES -- 2.1. Linear Spaces -- 2.2. 2-Norms and 2-Metrics -- 2.3. 2-Norms and Bivectors -- 2.4. Semi-2-Norms and Semi-2-Metrics -- 2.5. 2-Metrics in the Restricted Sense -- 2.6. Between Points and Midpoints -- 2.7. Properties (U) and (L) in Linear 2-Normed Spaces -- 2.8. Properties (U) and (L) in 2-Metric Spaces -- 2.9. Contribution to Non-Archimedean Functional Analysis -- CHAPTER 3.2-BANACH SPACES -- 3.1. Elementary Properties -- 3.2. Bounded Linear 2-Functionals -- 3.3. More Extensions of Bounded Linear 2-Functionals -- CHAPTER 4.COMPLETION OF LINEAR 2-NORMED SPACES -- 4.1. Elementary Properties -- 4.2. Completion of Linear 2-Normed Spaces -- 4.3. Relations between Banach Spaces and 2-Banach Spaces -- CHAPTER 5.2-INNER PRODUCT SPACES -- 5.1. 2-Inner Products -- 5.2. Generating 2-Inner Products -- 5.3. Generalizations of 2-Inner Products -- 5.4. 2-Inner Product Spaces and Gˆateaux Partial Derivatives -- CHAPTER 6.STRICT CONVEXITY -- 6.1. Elementary Characterizations -- 6.2. Strict Convexity by Duality Mappings -- 6.3. Strict Convexity by p-Semi-Inner Products -- 6.4. Strict Convexity by Algebraic and 2-Norm Midpoints -- 6.5. Strict Convexity in Topological Vector Spaces -- 6.6. 2-Norms Generated by Seminorms on the Space ofBivectors -- CHAPTER 7.STRICT 2-CONVEXITY -- 7.1. Elementary Characterizations -- 7.2. Strict 2-Convexity by Algebraic and 2-Norm Midpoints -- 7.3. Strict 2-Convexity by (α, β, γ)-2-Norm Interior Pointsand (α, β, γ)-Algebraic Interior Points -- 7.4. Strict 2-Convexity by Duality Mappings -- 7.5. Strict 2-Convexity by Extreme Points -- CHAPTER 8.UNIFORM CONVEXITY -- 8.1. Elementary Characterizations -- 8.2. Uniform Convexity In Quotient Spaces.

8.3. Uniform Convexity by 2-inner Products -- 8.4. Uniform Convexity by Bivectors -- 8.5. Uniform 2-Convexity in Linear 2-Normed Spaces -- CHAPTER 9.ISOMETRY CONDITIONS IN LINEAR 2-NORMED SPACES -- 9.1. Isometry Conditions -- 9.2. An Example of a Non-linear Isometry -- 9.3. Weak Conditions of Isometries -- 9.4. Non-expansive Mappings in Linear 2-Normed Spaces -- CHAPTER 10.ORTHOGONALITY RELATIONS BETWEENTHE NORMS AND 2-NORMS -- 10.1. Elementary Properties of Orthogonalities -- 10.2. Properties of Orthogonalities and the CharacterizationTheorem -- 10.3. The 2-Dimensional Case and Examples -- 10.4. Orthogonal Triples in Linear 2-Normed Spaces -- CHAPTER 11.QUADRATIC FORMS ON MODULES -- 11.1. Generalized A-Quadratic Forms of Type (P) -- 11.2. Generalized A-Quadratic Forms of Type (Q) -- 11.3. Applications -- 11.4. Extensions to Linear 2-Normed Spaces -- REFERENCES -- INDEX.

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