Open AccessFactorisation of orthogonal projectors
Author(s) -
Nataliia Sushchyk,
V. M. Degnerys
Publication year - 2021
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.55.2.181-187
Subject(s) - mathematics , projector , factorization , hilbert space , operator (biology) , banach space , pure mathematics , unitary operator , orthogonal basis , combinatorics , algebra over a field , discrete mathematics , computer science , algorithm , physics , chemistry , repressor , transcription factor , computer vision , gene , quantum mechanics , biochemistry
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, wegive an explicit formula for the operator $V$.