Geodesic
Every Invertible Hilbert Space Operator is a Product of Seven Positive Operators
Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 230-236

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that every invertible operator in a properly infinite von Neumann algebra, in particular in L(H) for infinite dimensional H, is a product of 7 positive invertible operators. This improves a result of Wu, who proved that every invertible operator in L(H) is a product of 17 positive invertible operators.
DOI : 10.4153/CMB-1995-033-9
Mots-clés : 47B99 
Phillips, N. Christopher. Every Invertible Hilbert Space Operator is a Product of Seven Positive Operators. Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 230-236. doi: 10.4153/CMB-1995-033-9
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[1] 1. Ballantine, C. S., Products of positive definite matrices IV, Linear Algebra Appl. 3(1970), 79–114. Google Scholar

[2] 2. Brown, A. and Pearcy, C., Multiplicative commutators of operators, Canad. J. Math. 18(1966), 737—749. Google Scholar

[3] 3. Fillmore, P. A., On products of symmetries, Canad. J. Math. 18(1966), 897–900. Google Scholar

[4] 4. Khalkali, M., Laurie, C., Mathes, B., and Radjavi, H., Approximation by products of positive operators, J. Operator Theory 29(1993), 237–247. Google Scholar

[5] 5. Phillips, N. C., Factorization problems in the invertible group of a homogeneous C*-algebra, Pacific J. Math., to appear. Google Scholar

[6] 6. Quinn, T., Factorization in C-Algebras: Products of Positive Operators, Ph.D. Thesis, Dalhousie University, Halifax, 1992. Google Scholar

[7] 7. Quinn, T., Products of decomposable positive operators, preprint. Google Scholar

[8] 8. Radjavi, H., On self-adjoint factorization of operators, Canad. J. Math. 21(1969), 1421–1426. Google Scholar

[9] 9. Sourour, A. R., A factorization theorem for matrices, Linear and Multilinear Algebra 19(1986), 141–147. Google Scholar

[10] 10. Wu, P. Y., Products of normal operators, Canad. J. Math. 40(1988), 1322–1330. Google Scholar

[11] 11 Wu, P. Y., The operator factorization problems, Linear Algebra Appl. 117(1989), 35—63. Google Scholar

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