The relationships between Invertible Module Maps X and X_z

2007/09/19 by Yun-Su Kim, Kim, Yun-Su
Mathematics · #46B15 #46C99 #46E20 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematics and Applications #Operator Algebras (math.OA) #math.FA #math.OA #msc:46B15 #msc:46C99 #msc:46E20

paper · pdf · doi:10.48550/arxiv.0709.2946

7 pages

openalex publication_date 2007/09/19 · arxiv created 2009/09/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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→M and X_z:R/R_z→M/M_z. In particular, for quasi-free Hilbert modules R and M, we provide a condition of a module map X:R→M, such that if X_z:R/R_z→M/M_z is invertible for every z in a domain Ω in the complex plane, then X is also invertible.

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