Characterizations of Operator Birkhoff–James Orthogonality
2017 ◽
Vol 60
(4)
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pp. 816-829
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Keyword(s):
New Type
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AbstractIn this paper, we obtain some characterizations of the (strong) Birkhoff–James orthogonality for elements of Hilbert C*-modules and certain elements of . Moreover, we obtain a kind of Pythagorean relation for bounded linear operators. In addition, for we prove that if the norm attaining set is a unit sphere of some finite dimensional subspace of and , then for every , T is the strong Birkhoff–James orthogonal to S if and only if there exists a unit vector such that . Finally, we introduce a new type of approximate orthogonality and investigate this notion in the setting of inner product C*-modules.
2020 ◽
2022 ◽
pp. 94-101
2020 ◽
1986 ◽
Vol 29
(1)
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pp. 15-21
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2017 ◽
Vol 103
(3)
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pp. 402-419
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2018 ◽
Vol 537
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pp. 348-357
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2008 ◽
Vol 2008
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pp. 1-6