Does Cauchy-Bunyakovsky-Schwarz inequality holds for semi-inner-product space, defined in https://en.wikipedia.org/wiki/Semi-inner-product#Semi-inner-products_for_Banach_spaces ?

I have found out in this case, $ <x,y><y,x> \leq <x,x><y,y>$

I have check other posts on MSE but all of them are based on different definition of semi inner product space.

Math newbie thanks you.

  • 5
    $\begingroup$ Isn't property (5) in the definition on that Wikipedia page exactly the Cauchy-Bunyakovsky-Schwarz inequality? $\endgroup$ – Robert Israel May 16 '17 at 0:35
  • 1
    $\begingroup$ Thanks for point that out. I thought [5] is a definition? Or could we prove this property [5] from the properties [1]-[4]? $\endgroup$ – High GPA May 16 '17 at 1:21
  • 1
    $\begingroup$ It's part of the definition. $\endgroup$ – Robert Israel May 16 '17 at 3:23

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