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Minimal projections onto subspaces of $l^{(n)}_\infty$ of codimension two

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Universitat de Barcelona
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Legacy

Abstract

Let $Y\subset l^{(n)}_\infty$ be one of its subspaces of codimension two. Denote by $\mathcal{P}_Y$ the set of all linear projections going from $l^{(n)}_\infty$ onto $Y$ . Put $$\lambda_Y = inf\{\parallel P\parallel : P\in\mathcal{P}_Y\}.$$ An operator $P_0\in\mathcal{P}_Y$ is called a minimal projection if $\parallel P_0\parallel = \lambda_Y$ . In this note we present a partial solution of the problem of calculation $\lambda_Y$ as well as the problem of calculation of minimal projection. We also characterize the unicity of minimal projection.

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