Interpolation of Schur multiplier spaces (Q1594987)

Let \(M(S_p)\) denote the space of Schur multipliers on the Schatten class \(S_p\). The author constructs a linear map which is a contraction on both \(M(S_2)\) and \(M(S_\infty)\) but which is not bounded in \(M(S_p)\) for any \(2< p<\infty\). Thus, \(M(S_p)\) is not an interpolation space between \(M(S_2)\) and \(M(S_\infty)\). There exists a corresponding result for completely bounded Fourier multipliers.