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Generalizations of the Triangle Inequality  
 
  Authors: Saburou Saitoh,  
  Keywords: Triangle inequality, Hilbert space, Sum of two Hilbert spaces, various operators among Hilbert spaces, Reproducing kernel, Linear mapping, Norm inequality  
  Date Received: 09/12/02  
  Date Accepted: 15/03/03  
  Subject Codes:

30C40, 46E32, 44A10, 35A22.

  
  Editors: Tsuyoshi Ando,  
 
  Abstract:

The triangle inequality is well-known and fundamental. Since the 8th General Inequalities meeting in Hungary (September 15-21, 2002), the author has been considering an idea that as triangle inequality, the inequality may be more suitable. The triangle inequality will be naturally generalized for some natural sum of any two members of any two Hilbert spaces . We shall introduce a natural sum Hilbert space for two arbitrary Hilbert spaces.
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