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 =
General
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