Let A and B be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.
@article{bwmeta1.element.doi-10_2478_conop-2012-0002,
author = {Mohammed Hichem Mortad},
title = {On the Normality of the Unbounded Product of Two Normal Operators},
journal = {Concrete Operators},
volume = {1},
year = {2013},
pages = {11-18},
zbl = {1293.47004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_conop-2012-0002}
}
Mohammed Hichem Mortad. On the Normality of the Unbounded Product of Two Normal Operators. Concrete Operators, Tome 1 (2013) pp. 11-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_conop-2012-0002/
Conway J.B., A Course in functional analysis, Springer, 1990 (2nd edition) | Zbl 0706.46003
Deutsch E., Gibson P.M., Schneider H., The Fuglede-Putnam theorem and normal products of matrices. Collection of articles dedicated to Olga Taussky Todd, Linear Algebra and Appl., 1976, 13/1-2, 53-58 | Zbl 0315.15013
Gheondea A., When are the products of normal operators normal? Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 2009, 52(100)/2, 129-150 | Zbl 1213.47021
Goldberg S., Unbounded linear operators, McGraw–Hill, 1966 | Zbl 0148.12501
Gustafson K., Positive (noncommuting) operator products and semi-groups, Math. Z., 1968, 105, 160-172 | Zbl 0159.43403
Gustafson K., On projections of selfadjoint operators, Bull. Amer. Math Soc., 1969, 75, 739-741 | Zbl 0177.17001
Kaplansky I., Products of normal operators, Duke Math. J., 1953, 20/2, 257-260 | Zbl 0050.34101
Kato T., Perturbation theory for linear operators, 2nd Edition, Springer, 1980 | Zbl 0435.47001
Kittaneh F., On the normality of operator products, Linear and Multilinear Algebra, 1991, 30/1-2, 1-4 | Zbl 0777.47017
Mortad M.H., An application of the Putnam-Fuglede theorem to normal products of self-adjoint operators, Proc. Amer. Math. Soc., 2003, 131/10, 3135-3141 | Zbl 1049.47019
Mortad M.H., On some product of two unbounded self-adjoint operators, Integral Equations Operator Theory, 2009, 64/3, 399-408 | Zbl 1241.47018
Mortad M.H., On the normality of the sum of two normal operators, Complex Anal. Oper. Theory, 2012, 6/1, 105-112.DOI: 10.1007/s11785-010-0072-7 [WoS][Crossref] | Zbl 1325.47050
Mortad M.H., On the closedness, the self-adjointness and the normality of the product of two unbounded operators, Demonstratio Math., 2012, 45/1, 161-167 | Zbl 1268.47002
Mortad M.H., An all-unbounded-operator version of the Fuglede-Putnam theorem, Complex Anal. Oper. Theory, (in press). DOI: 10.1007/s11785-011-0133-6 [WoS][Crossref]
Mortad M.H., Products of Unbounded Normal Operators. arXiv:1202.6143v1 | Zbl 1262.47008
Mortad M.H., The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness and Normality, (submitted). arXiv:1203.2545v1 | Zbl 1268.47002
Patel A., Ramanujan P.B., On sum and product of normal operators, Indian J. Pure Appl. Math., 1981, 12/10, 1213-1218 | Zbl 0469.47019
Rudin W., Functional analysis, McGraw-Hill, 1991 (2nd edition) | Zbl 0867.46001
Weidmann J., Linear operators in Hilbert spaces, Springer, 1980 | Zbl 0434.47001
Wiegmann N.A., Normal products of matrices, Duke Math J., 1948, 15, 633-638[Crossref][WoS] | Zbl 0031.24302
Wiegmann N.A., A note on infinite normal matrices, Duke Math. J., 1949, 16, 535-538 | Zbl 0035.19702