Segments of bounded linear idempotents on a Hilbert space |
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Authors: | Julien Giol |
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Affiliation: | LATP, Université Paul Cézanne, 13397 Marseille Cedex 20, France |
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Abstract: | Let H be a separable Hilbert space. We prove that any two homotopic idempotents in the algebra L(H) may be connected by a piecewise affine idempotent-valued path consisting of 4 segments at most. Moreover, we show that this constant is optimal provided H has infinite dimension. We also explain how this result is linked to the problem of finding common complements for two closed subspaces of H. |
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Keywords: | Idempotent Projection Piecewise affine homotopy Hilbert space geometry Common complement |
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