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    STUDIA MATHEMATICA - Issue no. 3 / 2006  
         
  Article:   ON THE CONVERSES OF THE REDUCTION PRINCIPLE IN INNER PRODUCT SPACES.

Authors:  COSTICĂ MUSTĂŢA. 		 
       
         
  Abstract:  Let H be an inner product space, X a complete subspace of H, and Y a closed subspace of X. The main result of this Note is the following converse of the Reduction Principle: if x0єX, hєHX and y0єY is the element of best approximation of both x0 and h, (x0 − h, x0 − y0) = 0 and codimXY = 1, then x0 is the element of best approximation of h in X.  
         
     
         
         
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