Amir

Characterizations of Inner Product Spaces

• Broschiertes Buch

Produktbeschreibung

Every mathematician working in Banaeh spaee geometry or Approximation theory knows, from his own experienee, that most "natural" geometrie properties may faH to hold in a generalnormed spaee unless the spaee is an inner produet spaee. To reeall the weIl known definitions, this means IIx 11 = , where is an inner (or: scalar) product on E, Le. a function from ExE to the underlying (real or eomplex) field satisfying: (i) O for x ~ o. (ii) is linear in x. (iii) = (intherealease,thisisjust =

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Produktdetails

• Operator Theory: Advances and Applications 20
• Verlag: Birkhäuser / Birkhäuser Basel / Springer, Basel
• Artikelnr. des Verlages: 978-3-0348-5489-4
• Softcover reprint of the original 1st ed. 1986
• Seitenzahl: 212
• Erscheinungstermin: 23. August 2014
• Englisch
• Abmessung: 244mm x 170mm x 12mm
• Gewicht: 375g
• ISBN-13: 9783034854894
• ISBN-10: 3034854897
• Artikelnr.: 41320370

Inhaltsangabe

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.