Journal of the
Korean Mathematical Society JKMS

Let $M$ be an invariant subspace of $H^2$ over the bidisk. Associated with $M$, we have the fringe operator $F^M_z$ on $M\om w M$. It is studied the Fredholmness of $F^M_z$ for (generalized) zero based invariant subspaces $M$. Also ${\rm ker}\, F^M_z$ and ${\rm ker}\, (F^M_z)^*$ are described.

Keywords: Hardy space over the bidisk, zero based invariant subspace, fringe operator, Fredholm operator, Fredholm index

MSC numbers: Primary 47A15, 32A35; Secondary 47B35