Characterizations of Inner Product Spaces

✍ Scribed by Prof. Dan Amir (auth.)

• Publisher: Birkhäuser Basel
• Year: 1986
• Tongue: English
• Leaves: 205
• Series: Operator Theory: Advances and Applications 20
• Edition: 1
• Category: Library

✦ Table of Contents

Front Matter....Pages i-vii
Introduction....Pages 1-5
Front Matter....Pages 7-7
The Parallelogram Equality and Derived Equalities....Pages 8-15
Norm Derivatives Characterizations....Pages 16-23
James’ Isoceles Orthogonality (Midpoints of Chords)....Pages 24-32
Birkhoff Orthogolaity....Pages 33-39
Best Approximation Characterizations....Pages 40-45
Loewner Ellipsoids and Parallelogram Inequalities....Pages 46-56
Pythagorean Type Orthogonalities....Pages 57-62
Area Arguments and Area Orthogonalities....Pages 63-69
Moduli of Convexity and Smoothness....Pages 70-76
The Rectangular Constant and Orthogonality In S E ....Pages 77-87
Inversions and Four-Point Properties....Pages 88-95
Front Matter....Pages 97-97
Kakutani’s conditions....Pages 98-106
3-Dimensional Approximation Properties....Pages 107-112
Blaschke’s Condition and Derived Characterizations....Pages 113-118
Chebyshev Radius and Centers....Pages 119-127
Combining the Garkavi-Klee Condition with the Hahn-Banach Theorem....Pages 128-133
Best Coapproximation and Optimal Sets....Pages 134-139
Symmetry of Orthogonality....Pages 140-148
Symmetry of Orthogonality with Smoothness....Pages 149-151
Front Matter....Pages 97-97
Subspace Homogeneity and Concluding Remarks....Pages 152-156
Back Matter....Pages 157-200

✦ Subjects

Science, general