Real Rank and Squaring Mapping for Unital C *-Algebras

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
A. "Alex" Chigogidze, Professor and Department Chair (Creator)
The University of North Carolina at Greensboro (UNCG )
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Abstract: It is proved that if X is a compact Hausdorff space of Lebesgue dimension dim(X), then the squaring mapping m: (C(X)sa)m ? C(X)+, defined by m(f1, . . . , fm) = Pm i=1 f2 i , is open if and only if m-1 = dim(X). Hence the Lebesgue dimension of X can be detected from openness of the squaring maps m. In the case m = 1 it is proved that the map x 7? x2, from the self-adjoint elements of a unital C-algebra A into its positive elements, is open if and only if A is isomorphic to C(X) for some compact Hausdorff space X with dim(X) = 0.

Additional Information

arXiv:math/0201214v1 [math.FA] 22 Jan 2002
Language: English
Date: 2002
Real rank, Bounded rank, Lebesgue dimension

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