  The first nearby very-low mass star planet-host discovered, TRAPPIST-1,
presents not only a unique opportunity for studying a system of multiple
terrestrial planets, but a means to probe magnetospheric interactions between a
star at the end of the main sequence and its close-in satellites. This
encompasses both the possibility of persistent coronal solar-like activity,
despite cool atmospheric temperatures, and the presence of large-scale
magnetospheric currents, similar to what is seen in the Jovian system.
Significantly, the current systems include a crucial role for close-in
planetary satellites analogous to the role played by the Galilean satellites
around Jupiter. We present the first radio observations of the seven-planet
TRAPPIST-1 system using the Karl G. Jansky Very Large Array, looking for both
highly circularly polarized radio emission and/or persistent quiescent
emissions. We measure a broadband upper flux density limit of <8.1 $\mu$Jy
across 4-8 GHz, and place these observations both in the context of
expectations for stellar radio emission, and the possible electrodynamic
engines driving strong radio emissions in very-low mass stars and brown dwarfs,
with implications for future radio surveys of TRAPPIST-1 like planet-hosts. We
conclude that magnetic activity of TRAPPIST-1 is predominantly coronal and does
not behave like the strong radio emitters at the stellar/sub-stellar boundary.
We further discuss the potential importance of magnetic field topology and
rotation rates, demonstrating that a TRAPPIST-1 like planetary system around a
rapidly rotating very-low mass star can generate emission consistent with the
observed radio luminosities of very-low mass stars and brown dwarfs.
