A morphism $f\colon X\to Y$ of spectra such that for every integer $n$ the induced map $\pi_n(f)\colon\pi_n(X)\to\pi_n(Y)$ on stable homotopy groups is zero is called a *ghost map*.

Not every ghost map $f$ is the zero object of the abelian group $\operatorname{Hom}_{SH}(X,Y)$ (more precisely, its image $\bar f\in \operatorname{Hom}_{SH}(X,Y)$ in the stable homotopy category $SH$).

Suppose $X=\Sigma^\infty A$ and $Y=\Sigma^\infty B$ are the suspension spectra of

finiteCW-complexes, let $f=\Sigma^\infty f'$ for a map $f'\colon A'\to B'$ and suppose that $f$ is a ghost map. Is $f$ necessarily zero in this case?