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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 Published:
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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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