Amir
Birkhäuser Basel
0e druk, 2014
9783034854894
Characterizations of Inner Product Spaces
Specificaties
Paperback, 200 blz.
|
Engels
Birkhäuser Basel |
2014
ISBN13: 9783034854894
Rubricering
Onderdeel van serie
Operator Theory: Advances and Applications
Verwachte levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
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 =
Specificaties
ISBN13:9783034854894
Taal:Engels
Bindwijze:paperback
Aantal pagina's:200
Uitgever:Birkhäuser Basel
Druk:0
Inhoudsopgave
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.