A class of simple tracially AF -algebras.
Livingston, N.E. (2002)
International Journal of Mathematics and Mathematical Sciences
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Livingston, N.E. (2002)
International Journal of Mathematics and Mathematical Sciences
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Marius Dadarlat, Terry A. Loring (1994)
Annales de l'institut Fourier
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G. Elliott extended the classification theory of -algebras to certain real rank zero inductive limits of subhomogeneous -algebras with one dimensional spectrum. We show that this class of -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the -group. Perturbation and lifting results are provided for certain subhomogeneous -algebras.
Hans Havlicek, Peter Šemrl (2006)
Studia Mathematica
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We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.
B. Blackadar, M. Dadarlat, M. Rordam (1991)
Mathematica Scandinavica
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Bernard Aupetit, H. Mouton (1996)
Studia Mathematica
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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.
Bruce Blackadar, Ola Bratteli (1992)
Mathematische Annalen
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Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.
Robert J. Archbold, Eberhard Kaniuth (2006)
Studia Mathematica
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Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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Stacey, P.J. (2006)
The New York Journal of Mathematics [electronic only]
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