Abstract
In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss' famous result on the denseness of norm attaining operators. Specifically, we show given any A∈ L( H) there is a sequence of rank-1 operators K n such that A+K n is norm attaining for each n and K n converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operator-valued functions.
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