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Volume 7, Issue 2, Article 57 |
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Relation Between Best Approximant and Orthogonality in $C_1$-classes
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Authors: |
Mecheri Salah, |
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Keywords:
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Best approximant, Schatten $p$-classes, Orthogonality, $varphi$-Gateaux derivative. |
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Date Received:
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21/05/05 |
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Date Accepted:
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13/03/06 |
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Subject Codes: |
Primary 41A52, 41A35, 47B47; Secondary 4
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Editors: |
Gradimir V. Milovanovic, |
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Abstract: |
Let  be a complex Banach space and let  be subspace of . In this paper we characterize the best approximant to  from and we prove the uniqueness, in terms of a new concept of derivative. Using this result we establish a new characterization of the best- approximation to  (trace class) from . Then, we apply these results to characterize the operators which are orthogonal in the sense of Birkhoff.
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