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Volume 4, Issue 3, Article 62 |
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Generalizations of the Triangle Inequality
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Authors: |
Saburou Saitoh, |
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Keywords:
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Triangle inequality, Hilbert space, Sum of two Hilbert spaces, various operators among Hilbert spaces, Reproducing kernel, Linear mapping, Norm inequality |
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Date Received:
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09/12/02 |
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Date Accepted:
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15/03/03 |
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Subject Codes: |
30C40, 46E32, 44A10, 35A22.
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Editors: |
Tsuyoshi Ando, |
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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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