On the \(\mathop\leq\limits^\sharp\)-order on the set of linear bounded operators in Banach space (Q358181)
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scientific article; zbMATH DE number 6198920
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(\mathop\leq\limits^\sharp\)-order on the set of linear bounded operators in Banach space |
scientific article; zbMATH DE number 6198920 |
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On the \(\mathop\leq\limits^\sharp\)-order on the set of linear bounded operators in Banach space (English)
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16 August 2013
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Extending the relation \(\leq ^{\sharp}\) defined by \textit{S. K. Mitra} [Linear Algebra Appl. 92, 17--37 (1987; Zbl 0619.15006)] from \(M_n(\mathbb C)\) to \(B(X)\), the author defines for \(A,B\in B(X)\) that \(A\leq^{\sharp} B\) if there exists an idempotent \(P\in B(X)\) such that \(\overline{\text{im}A}= \text{im}P\), \(\ker A =\ker P\), \(PA = PB\), and \(AP = BP\), and shows that \(\leq^{\sharp}\) is a partial order on \(B(X)\).
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linear bounded operator
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Banach space
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matrix \(\mathop\leq\limits^\sharp\)-order
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matrix \(\overline\leq\)-order
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group inverse matrix
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index of a matrix
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Hilbert space
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idempotent
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