# On the Normality of the Unbounded Product of Two Normal Operators

Concrete Operators (2013)

- Volume: 1, page 11-18
- ISSN: 2299-3282

## Access Full Article

top## Abstract

top## How to cite

topMohammed Hichem Mortad. "On the Normality of the Unbounded Product of Two Normal Operators." Concrete Operators 1 (2013): 11-18. <http://eudml.org/doc/266903>.

@article{MohammedHichemMortad2013,

abstract = {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.},

author = {Mohammed Hichem Mortad},

journal = {Concrete Operators},

keywords = {Unbounded Operators; Normal Operators; Fuglede-Putnam Theorem; unbounded operators; normal operators; Fuglede-Putnam theorem},

language = {eng},

pages = {11-18},

title = {On the Normality of the Unbounded Product of Two Normal Operators},

url = {http://eudml.org/doc/266903},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Mohammed Hichem Mortad

TI - On the Normality of the Unbounded Product of Two Normal Operators

JO - Concrete Operators

PY - 2013

VL - 1

SP - 11

EP - 18

AB - 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.

LA - eng

KW - Unbounded Operators; Normal Operators; Fuglede-Putnam Theorem; unbounded operators; normal operators; Fuglede-Putnam theorem

UR - http://eudml.org/doc/266903

ER -

## References

top- Conway J.B., A Course in functional analysis, Springer, 1990 (2nd edition) Zbl0706.46003
- 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 Zbl0315.15013
- Gheondea A., When are the products of normal operators normal? Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 2009, 52(100)/2, 129-150 Zbl1213.47021
- Goldberg S., Unbounded linear operators, McGraw–Hill, 1966 Zbl0148.12501
- Gustafson K., Positive (noncommuting) operator products and semi-groups, Math. Z., 1968, 105, 160-172 Zbl0159.43403
- Gustafson K., On projections of selfadjoint operators, Bull. Amer. Math Soc., 1969, 75, 739-741 Zbl0177.17001
- Kaplansky I., Products of normal operators, Duke Math. J., 1953, 20/2, 257-260 Zbl0050.34101
- Kato T., Perturbation theory for linear operators, 2nd Edition, Springer, 1980 Zbl0435.47001
- Kittaneh F., On the normality of operator products, Linear and Multilinear Algebra, 1991, 30/1-2, 1-4 Zbl0777.47017
- 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 Zbl1049.47019
- Mortad M.H., On some product of two unbounded self-adjoint operators, Integral Equations Operator Theory, 2009, 64/3, 399-408 Zbl1241.47018
- 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] Zbl1325.47050
- 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 Zbl1268.47002
- 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 Zbl1262.47008
- Mortad M.H., The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness and Normality, (submitted). arXiv:1203.2545v1 Zbl1268.47002
- Patel A., Ramanujan P.B., On sum and product of normal operators, Indian J. Pure Appl. Math., 1981, 12/10, 1213-1218 Zbl0469.47019
- Rudin W., Functional analysis, McGraw-Hill, 1991 (2nd edition) Zbl0867.46001
- Weidmann J., Linear operators in Hilbert spaces, Springer, 1980 Zbl0434.47001
- Wiegmann N.A., Normal products of matrices, Duke Math J., 1948, 15, 633-638[Crossref][WoS] Zbl0031.24302
- Wiegmann N.A., A note on infinite normal matrices, Duke Math. J., 1949, 16, 535-538 Zbl0035.19702

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.