  We revisit tensor algebras of subproduct systems with Hilbert space fibers,
resolving some open questions in the case of infinite dimensional fibers. We
characterize when a tensor algebra can be identified as the algebra of
uniformly continuous noncommutative functions on a noncommutative homogeneous
variety or, equivalently, when it is residually finite dimensional: this
happens precisely when the closed homogeneous ideal associated to the
subproduct system satisfies a Nullstellensatz with respect to the algebra of
uniformly continuous noncommutative functions on the noncommutative closed unit
ball. We show that - in contrast to the finite dimensional case - in the case
of infinite dimensional fibers this Nullstellensatz may fail. Finally, we also
resolve the isomorphism problem for tensor algebras of subproduct systems: two
such tensor algebras are (isometrically) isomorphic if and only if their
subproduct systems are isomorphic in an appropriate sense.
