Displaying similar documents to “Weakly mixing rank-one transformations conjugate to their squares”

Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples

María Burgos, Jorge J. Garcés, Antonio M. Peralta (2011)

Studia Mathematica

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We prove that every biorthogonality preserving linear surjection from a weakly compact JB*-triple containing no infinite-dimensional rank-one summands onto another JB*-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW*-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW*-triples containing no rank-one summands are isomorphic if and only if there...

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.

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.

Weak Closure Theorem fails for ℤ²-actions

T. Downarowicz, J. Kwiatkowski (2002)

Studia Mathematica

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We construct an example of a Morse ℤ²-action which has rank one and whose centralizer contains elements which cannot be weakly approximated by the transformations of the action.

Mixing on rank-one transformations

Darren Creutz, Cesar E. Silva (2010)

Studia Mathematica

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We prove that mixing on rank-one transformations is equivalent to "the uniform convergence of ergodic averages (as in the mean ergodic theorem) over subsequences of partial sums". In particular, all polynomial staircase transformations are mixing.