New characterizations of EP, generalized normal and generalized Hermitian elements in rings (Q428064)
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scientific article; zbMATH DE number 6047680
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New characterizations of EP, generalized normal and generalized Hermitian elements in rings |
scientific article; zbMATH DE number 6047680 |
Statements
New characterizations of EP, generalized normal and generalized Hermitian elements in rings (English)
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19 June 2012
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EP elements
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Moore-Penrose inverse
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group inverse
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generalized normal elements
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generalized Hermitian elements
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ring with involution
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Drazin inverse
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Complex matrices and Hilbert space operators \(A\) with closed ranges for which the ranges of \(A\) and \(A^*\) coincide are said to have the property EP. Examples are Hermitian, normal and nonsingular matrices (operators). Such matrices and operators have been studied by many authors. In rings with involution, EP elements are those for which the Drazin and Moore-Penrose inverses exist and coincide.NEWLINENEWLINE In this paper, the authors study the EP elements of such rings and present new characterizations in purely algebraic forms. They also introduce and study generalized normal and generalized Hermitian elements in rings and present several new characterizations for elements in rings with involution to be normal or Hermitian.
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