  We study Toeplitz operators with respect to a commuting $n$-tuple of bounded
operators which satisfies some additional conditions coming from complex
geometry. Then we consider a particular such tuple on a function space. The
algebra of Toeplitz operators with respect to that particular tuple becomes
naturally homeomorphic to $L^\infty$ of a certain compact subset of $\mathbb
C^n$. Dual Toeplitz operators are characterized. En route, we prove an
extension type theorem which is not only important for studying Toeplitz
operators, but also has an independent interest because dilation theorems do
not hold in general for $n>2$.
