Eberlein almost periodic functions that are not pseudo almost periodic

We construct Eberlein almost periodic functions $f_j:J\to H$ so that $\mathrm{\mid }\mathrm{\mid }{f}_1(\cdot )\mathrm{\mid }\mathrm{\mid }$ is not ergodic and thus not Eberlein almost periodic and $\mathrm{\mid }\mathrm{\mid }{f}_2(\mathrm{.})\mathrm{\mid }\mathrm{\mid }$ is Eberlein almost periodic, but $f_1$ and $f_2$ are not pseudo almost periodic, the Parseval equation for them fails, where J=\r_+ or \r and $H$ is a Hilbert space. This answers several questions posed by Zhang and Liu [18].