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Minimal projections in tensor-product spaces. (English) Zbl 0594.46061

This paper takes an old result due to Rudin in 1962 about the existence of bounded projections from \(L_ 1\) onto \(H_ 1\). An elementary observation that this result can also be applied to minimal projections is made. The main application of this observation is more profound and takes place in a tensor product space. This application is used to derive old and new results about projection constants and minimal projections.

MSC:

46M05 Tensor products in functional analysis
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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References:

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