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.
@article{bwmeta1.element.bwnjournal-article-apmv66z1p43bwm,
author = {Douglas N. Clark},
title = {Projectivity and lifting of Hilbert module maps},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {43-48},
zbl = {0873.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p43bwm}
}
Douglas N. Clark. Projectivity and lifting of Hilbert module maps. Annales Polonici Mathematici, Tome 66 (1997) pp. 43-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p43bwm/
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[001] [2] J. F. Carlson, D. N. Clark, C. Foiaş and J. P. Williams, Projective Hilbert 𝔸(𝔻)-modules, New York J. Math. 1 (1994), 26-38. | Zbl 0812.46043
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