# Projectivity and lifting of Hilbert module maps

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 43-48
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topDouglas N. Clark. "Projectivity and lifting of Hilbert module maps." Annales Polonici Mathematici 66.1 (1997): 43-48. <http://eudml.org/doc/270024>.

@article{DouglasN1997,

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.},

author = {Douglas N. Clark},

journal = {Annales Polonici Mathematici},

keywords = {Hilbert module; lifting theorem; polynomially bounded; isometric Hilbert modules; projective; category of Hilbert modules similar to contractive ones; similarity to a contraction; operator matrix},

language = {eng},

number = {1},

pages = {43-48},

title = {Projectivity and lifting of Hilbert module maps},

url = {http://eudml.org/doc/270024},

volume = {66},

year = {1997},

}

TY - JOUR

AU - Douglas N. Clark

TI - Projectivity and lifting of Hilbert module maps

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 43

EP - 48

AB - 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.

LA - eng

KW - Hilbert module; lifting theorem; polynomially bounded; isometric Hilbert modules; projective; category of Hilbert modules similar to contractive ones; similarity to a contraction; operator matrix

UR - http://eudml.org/doc/270024

ER -

## References

top- [1] J. F. Carlson and D. N. Clark, Cohomology and extensions of Hilbert modules, J. Funct. Anal. 128 (1995), 278-306. Zbl0833.46038
- [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. Zbl0812.46043
- [3] R. G. Douglas and V. I. Paulsen, Hilbert Modules over Function Algebras, Longman Scientific and Technical, New York, 1989.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.