| Kaplansky Density and Kadison Transitivity Theorems for Irreducible Representations of Real C＊-Algebras |
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| 作者姓名： | Jeffrey L. BOERSEMA |
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| 作者单位： | Department of Mathematics, Seattle University, Seattle, WA 98122, USA |
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| 摘 要： | We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.
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| 关 键 词： | C＊代数 不可约分表示 转移性 密度 |
| 收稿时间： | 27 April 2005 |
| 修稿时间： | 2005-04-27 |
Kaplansky Density and Kadison Transitivity Theorems for
Irreducible Representations of Real <Emphasis Type="Italic">C</Emphasis>*-Algebras |
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| Jeffrey L. BOERSEMA.Kaplansky Density and Kadison Transitivity Theorems for
Irreducible Representations of Real C*-Algebras[J].Acta Mathematica Sinica,2007,23(10):1827-1832. |
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| Authors: | Jeffrey L Boersema |
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| Institution: | (1) Department of Mathematics, Seattle University, Seattle, WA 98122, USA |
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| Abstract: | We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem
for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra
is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or
quaternionic structure with respect to which the density and transitivity theorems hold. |
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| Keywords: | real C*-algebra irreducible * representation transitivity |
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