Pixel connectivity
In operator theory, an area of mathematics, Douglas' lemma relates factorization, range inclusion, and majorization of Hilbert space operators. It is generally attributed to Ronald G. Douglas, although Douglas acknowledges that aspects of the result may already have been known. The statement of the result is as follows:
Theorem: If A and B are bounded operators on a Hilbert space H, the following are equivalent:
Moreover, if these equivalent conditions hold, then there is a unique operator C such that
See also
References
- Douglas, R.G.: "On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space". Proceedings of the American Mathematical Society 17, 413–415 (1966)