## A space by W. Gowers and new results on norm and numerical radius attaining operators.(English)Zbl 0786.47002

Summary: We use a Banach space recently considered by W. Gowers to improve some results on norm attaining operators. In fact we show that the norm attaining operators from this space to a strictly convex Banach space are finite-rank. The same Banach space is also used to get a new example of a space which does not satisfy the denseness of the numerical radius attaining operators. This new counterexample improves and simplifies the one previously obtained by R. Payá, who answered an open question raised by B. Sims in 1972.