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Turkish Journal of Mathematics

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

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1110

Last Page

1113

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