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ArticleOriginal scientific text

Title

Geometry of oblique projections

Authors 1, 2, 2

Affiliations

  1. Instituto de Ciencias, Univ. Nac de Gral. Sarmiento, Roca 850, (1663) San Miguel, Pcia. de Buenos Aires, Argentina
  2. Instituto Argentino de Matemática, Saavedra 15 3er piso,(1083) Buenos Aires, Argentina

Abstract

Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections Pa determined by the different involutions #a induced by positive invertible elements a ∈ A. The maps φ:P→Pa sending p to the unique q∈Pa with the same range as p and Ωa:Pa→Pa sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q,r ∈ A with ||q-r|| < 1 such that there exists a positive element a ∈ A satisfying q,r∈Pa. In this case q and r can be joined by a unique short geodesic along the space of idempotents Q of A.

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Studia Mathematica
1999/137/1
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Pages:
61-79
Main language of publication
English
Received
1998-09-25
Published
1999
Exact and natural sciences