Projectivity and lifting of Hilbert module maps
Volume 66 / 1997
Annales Polonici Mathematici 66 (1997), 43-48
DOI: 10.4064/ap-66-1-43-48
Abstract
In a recent paper, Carlson, Foiaş, Williams and the author proved that isometric Hilbert modules are projective in the category of Hilbert modules similar to contractive ones. In this paper, a simple proof, based on a strengthened lifting theorem, is given. The proof also applies to an equivalent theorem of Foiaş and Williams on similarity to a contraction of a certain 2 × 2 operator matrix.
