The relationships between Invertible Module Maps X and X_z

Details The relationships between Invertible Module Maps X and X_z The relationships between Invertible Module Maps X and X_z

2007-09-19

arxiv.org/abs/0709.2946v2

Mathematics

Functional Analysis

7 pages

Scientific paper

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.

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