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Proceedings of the London Mathematical Society Advance Access originally published online on June 2, 2009
Proceedings of the London Mathematical Society 2009 99(3):757-786; doi:10.1112/plms/pdp017
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© 2009 London Mathematical Society

A solution to the Douglas–Rudin problem for matrix-valued functions

Steven Barclay

School of Mathematics
University of Leeds
Leeds
LS2 9JT
United Kingdom
steven@datanet.org.uk

Received 12 June 2007. Revision received 4 February 2009.

We solve the noncommutative Douglas–Rudin problem, showing that any log-integrable essentially bounded square matrix-valued function f can be written in the form h*g, where h and g lie in H {infty}. Extensions to other L p spaces, with norm bounds on the factors of f, are also provided.

2000 Mathematics Subject Classification 47A68 (primary), 46E40, 30D55 (secondary).


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