Factorisation of orthogonal projectors

  • N. S. Sushchyk Ivan Franko National University of Lviv, Lviv, Ukraine
  • V. M. Degnerys Peeklogic, Lviv, Ukraine
Keywords: special factorisation, orthogonal projector


We study the problem of a special factorisation of an orthogonal projector~$P$ acting in the Hilbert space $L_2(\mathbb R)$ with $\dim\ker P<\infty$. In particular, we prove that the orthogonal projector~$P$ admits a special factorisation in the form
$P=VV^*$, where $V$ is an isometric upper-triangular operator in the Banach algebra of all linear continuous operators in $L_2(\mathbb R)$. Moreover, we
give an explicit formula for the operator $V$.


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How to Cite
Sushchyk NS, Degnerys VM. Factorisation of orthogonal projectors. Mat. Stud. [Internet]. 2021Jun.22 [cited 2021Dec.7];55(2):181-7. Available from: http://www.matstud.org.ua/ojs/index.php/matstud/article/view/210