The main result of this paper is that every normal operator on an infinitedimensional (complex) Hilbert space H is the product of four self-adjoint operators; our Theorem 4 is an actually stronger result. A large class of normal operators will be given which cannot be expressed as the product of three self-adjoint operators.This work was motivated by a well-known resul t of Halmos and Kakutani (3) that every unitary operator on H is the product of four symmetries, i.e., operators that are self-adjoint and unitary.1. By “operator” we shall mean bounded linear operator. The space H will be infinite-dimensional (separable or non-separable) unless otherwise specified. We shall denote the class of self-adjoint operators on H by and that of symmetries by .
Radjavi, Heydar. On Self-Adjoint Factorization of Operators. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1421-1426. doi: 10.4153/CJM-1969-156-6
@article{10_4153_CJM_1969_156_6,
author = {Radjavi, Heydar},
title = {On {Self-Adjoint} {Factorization} of {Operators}},
journal = {Canadian journal of mathematics},
pages = {1421--1426},
year = {1969},
volume = {21},
number = {1},
doi = {10.4153/CJM-1969-156-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-156-6/}
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