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Summer 2019 Special factors of invertible elements in simple unital purely infinite $C^*$-algebras
Ahmed Al-Rawashdeh
Adv. Oper. Theory 4(3): 641-650 (Summer 2019). DOI: 10.15352/aot.1810-1432

Abstract

In simple unital purely infinite $C^*$-algebra $A$‎, ‎Leen proved that any element in the identity component of the invertible group is‎ ‎a finite product of symmetries of $A$‎. ‎Revising Leen's factorization‎, ‎we show that a multiple of eight of such factors are $*$-symmetries of the form $1-2P_{i,j}(u)$‎, ‎where $P_{i,j}(u)$ are certain projections of the $C^*$-matrix algebra‎, ‎defined by Dye as‎ ‎\begin{equation*}‎ ‎P_{i,j}(u) = \frac{1}{2}(e_{i,i}+e_{j,j}‎ ‎+e_{i,1}ue_{1,j}+e_{j,1}u^*e_{1,i}),‎ ‎\end{equation*}‎ ‎for a given system of matrix units $\{e_{i,j}\}_{i,j=1}^n$ of $A$ and a unitary $u\in \mathcal{U}(A)$‎. ‎

Citation

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Ahmed Al-Rawashdeh. "Special factors of invertible elements in simple unital purely infinite $C^*$-algebras." Adv. Oper. Theory 4 (3) 641 - 650, Summer 2019. https://doi.org/10.15352/aot.1810-1432

Information

Received: 28 October 2018; Accepted: 9 January 2019; Published: Summer 2019
First available in Project Euclid: 2 March 2019

zbMATH: 07056790
MathSciNet: MR3919036
Digital Object Identifier: 10.15352/aot.1810-1432

Subjects:
Primary: 46L05
Secondary: 46L80

Keywords: ‎ invertible group , $C^*$-Algebras , symmetry

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 3 • Summer 2019
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