The relationships between Invertible Module Maps X and X_z

Abstract

If $R$ and $M$ are Hilbert modules (in the sense of R. G. Douglas and V. I. Paulsen), we study the relationship between invertible module maps $X:R\to M$ and $X_z:R/R_z\to M/M_z$. In particular, for quasi-free Hilbert modules $R$ and $M$, we provide a condition of a module map $X:R\to M$, such that if $X_z:R/R_z\to M/M_z$ is invertible for every $z$ in a domain $\Omega$ in the complex plane, then $X$ is also invertible.

7 pages

References in corpus (1)

• On quasi-free Hilbert modules