  We study the link between Wick, anti-Wick and analytic kernel operators on
the Bargmann transform side. We find classes of kernels, e.g. $\wideparen
{\mathcal B} _s$, whose corresponding operators agree with the sets of linear
and continuous operators on $\mathcal A _s$, the images of Pilipovi{\'c} under
the Bargmann transform. We show that in several situations, the sets of Wick,
anti-Wick and kernel operators with symbols and kernels in $\wideparen
{\mathcal B} _s$ agree. We also show some ring, module and composition
properties for $\wideparen {\mathcal B} _s$, and similarly for other spaces
related to $\wideparen {\mathcal B} _s$.
