Characterizations of Inner Product Spaces

Inhaltsverzeichnis

• 2-Dimensional Characterization.
• The Parallelogram Equality and Derived Equalities.
• Norm Derivatives Characterizations.
• James’ Isoceles Orthogonality (Midpoints of Chords).
• Birkhoff Orthogolaity.
• Best Approximation Characterizations.
• Loewner Ellipsoids and Parallelogram Inequalities.
• Pythagorean Type Orthogonalities.
• Area Arguments and Area Orthogonalities.
• Moduli of Convexity and Smoothness.
• The Rectangular Constant and Orthogonality In S E.
• Inversions and Four-Point Properties.
• 3 - Dimensional Characterization.
• Kakutani’s conditions.
• 3-Dimensional Approximation Properties.
• Blaschke’s Condition and Derived Characterizations.
• Chebyshev Radius and Centers.
• Combining the Garkavi-Klee Condition with the Hahn-Banach Theorem.
• Best Coapproximation and Optimal Sets.
• Symmetry of Orthogonality.
• Symmetry of Orthogonality with Smoothness.
• Subspace Homogeneity and Concluding Remarks.