On a factorization of operators on finite dimensional Hilbert spaces

Authors

JIAWEI LUO
JUEXIAN LI
GENG TIAN

DOI

10.3906/mat-1507-4

Abstract

As is well known, for any operator $T$ on a complex separable Hilbert space, $T$ has the polar decomposition $T=U T $, where $U$ is a partial isometry and $ T $ is the nonnegative operator $(T^*T)^{\frac{1}{2}}$. In 2014, Tian et al. proved that on a complex separable infinite dimensional Hilbert space, any operator admits a polar decomposition in a strongly irreducible sense. More precisely, for any operator $T$ and any $\varepsilon>0$, there exists a decomposition $T=(U+K)S$, where $U$ is a partial isometry, $K$ is a compact operator with $ K

Keywords

Polar decomposition, strongly irreducible operator, Jordan block

First Page

1110

Last Page

1113

Recommended Citation

LUO, JIAWEI; LI, JUEXIAN; and TIAN, GENG (2016) "On a factorization of operators on finite dimensional Hilbert spaces," Turkish Journal of Mathematics: Vol. 40: No. 5, Article 16. https://doi.org/10.3906/mat-1507-4
Available at: https://journals.tubitak.gov.tr/math/vol40/iss5/16