Abstract.
In this paper we will prove that an averaging projection P a : K (H) → Y, given by the formula \(P_a(A)=\frac{A+A^T}{2}\), is the only norm-one projection. Here, K (H) is a space of compact operators on a separable real Hilbert space H, and Y is the subspace of K(H) consisting of all symmetric operators.
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Author’s address: Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
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Mielczarek, D. The unique minimality of an averaging projection. Monatsh Math 154, 157–171 (2008). https://doi.org/10.1007/s00605-008-0527-3
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DOI: https://doi.org/10.1007/s00605-008-0527-3