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Nests with the partial factorization property

Authors:	Guoxing Ji Xiuhong Sun

Institution:	College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, People's Republic of China ; College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, People's Republic of China

Abstract:	It is proved that a nest $\mathcal N$ on a separable complex Hilbert space $\mathcal H$ has the left (resp. right) partial factorization property, which means that for every invertible operator from $\mathcal H$ onto a Hilbert space $\mathcal K$ there exists an isometry (resp. a coisometry) from $\mathcal H$ into $\mathcal K$ such that both and $T^{-1}U$ are in the associated nest algebra $Alg \mathcal N$ if and only if it is atomic (resp. countable).

Keywords:	Nest nest algebra left (resp right) partial factorization factorization

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