 

Jon F. Carlson, Douglas N. Clark, Ciprian Foias, and J.P. Williams
Projective Hilbert A(D)Modules


Published: 
August 10, 1994 
Keywords: 
Hilbert module, projective, lifting theorem, polynomially bounded operator, cramped Hilbert module 
Subject: 
Primary: 47D, Secondary: 47C 


Abstract
Let C denote the category of Hilbert modules which are
similar to contractive Hilbert modules. It is proved that if H_{0}
, H ∈ C and if H_{1} is similar to an isometric Hilbert
module, then the sequence
0 → H_{0} → H → H_{1} → 0
splits. Thus the isometric Hilbert modules are projective in
C. It follows that Ext^{n}_{C} (K, H) = 0, whenever
n > 1, for H, K ∈ C. In addition, it is proved that
(Hilbert modules similar to) unitary Hilbert modules are projective
in the category H of all Hilbert modules. Connections with
the conjecture that C is a proper subset of
H are discussed.


Acknowledgements
The first and third authors were partially supported by NSF grants. 

Author information
Jon F. Carlson:
Department of Mathematics, University of Georgia, Athens,
GA 30602
jfc@math.uga.edu
http://www.math.uga.edu/~jfc/
Douglas N. Clark:
Department of Mathematics, University of Georgia, Athens,
GA 30602
dnc@joe.math.uga.edu
Ciprian Foias:
Department of Mathematics, Indiana University,
Bloomington, IN 47405
foias@indiana.edu

