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Norm derivatives and characterizations of inner product spaces /
The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces. Since the appearance of Jordan-von Neumann's classical theorem...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2010.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Introduction. Historical notes
- Normed linear spaces
- Strictly convex normed linear spaces
- Inner product spaces
- Orthogonalities in normed linear spaces
- Norm derivatives. Norm derivatives : definition and basic properties
- Orthogonality relations based on norm derivatives
- p'[symbol]-orthogonal transformations
- On the equivalence of two norm derivatives
- Norm derivatives and projections in normed linear spaces
- Norm derivatives and Lagrange's identity in normed linear spaces
- On some extensions of the norm derivatives
- p-orthogonal additivity
- Norm derivatives and heights. Definition and basic properties
- Characterizations of inner product spaces involving geometrical properties of a height in a triangle
- Height functions and classical orthogonalities
- A new orthogonality relation
- Orthocenters
- A characterization of inner product spaces involving an isosceles trapezoid property
- Functional equations of the height transform
- Perpendicular bisectors in Normed spaces. Definitions and basic properties
- A new orthogonality relation
- Relations between perpendicular bisectors and classical orthogonalities
- On the radius of the circumscribed circumference of a triangle
- Circumcenters in a triangle
- Euler line in real normed space
- Functional equation of the perpendicular bisector transform
- Bisectrices in real Normed spaces. Bisectrices in real normed spaces
- A new orthogonality relation
- Functional equation of the bisectrix transform
- Generalized bisectrices in strictly convex real normed spaces
- Incenters and generalized bisectrices
- Areas of triangles in Normed spaces. Definition of four areas of triangles
- Classical properties of the areas and characterizations of inner product spaces
- Equalities between different area functions
- The area orthogonality.