Displaying similar documents to “Notes on a class of simple C*-algebras with real rank zero.”

Extensions of certain real rank zero C * -algebras

Marius Dadarlat, Terry A. Loring (1994)

Annales de l'institut Fourier

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G. Elliott extended the classification theory of A F -algebras to certain real rank zero inductive limits of subhomogeneous C * -algebras with one dimensional spectrum. We show that this class of C * -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the K 1 -group. Perturbation and lifting results are provided for certain subhomogeneous C * -algebras.

From geometry to invertibility preservers

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.

Trace and determinant in Banach algebras

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.

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that rank ( P * A Q ) = rank ( P * A ) + rank ( A Q ) - rank ( A ) , where A is idempotent, [ P , Q ] has full row rank and P * Q = 0 . Some applications of the rank formula to generalized inverses of matrices are also presented.

Stable rank and real rank of compact transformation group C*-algebras

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.