Denseness for norm attaining operator-valued functions Original Research Article

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