On the Normality of the Unbounded Product of Two Normal Operators

Mohammed Hichem Mortad

Concrete Operators (2013)

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

Abstract

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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.

How to cite

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Mohammed 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

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  1. Conway J.B., A Course in functional analysis, Springer, 1990 (2nd edition) Zbl0706.46003
  2. 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
  3. 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
  4. Goldberg S., Unbounded linear operators, McGraw–Hill, 1966 Zbl0148.12501
  5. Gustafson K., Positive (noncommuting) operator products and semi-groups, Math. Z., 1968, 105, 160-172 Zbl0159.43403
  6. Gustafson K., On projections of selfadjoint operators, Bull. Amer. Math Soc., 1969, 75, 739-741 Zbl0177.17001
  7. Kaplansky I., Products of normal operators, Duke Math. J., 1953, 20/2, 257-260 Zbl0050.34101
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  9. Kittaneh F., On the normality of operator products, Linear and Multilinear Algebra, 1991, 30/1-2, 1-4 Zbl0777.47017
  10. 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
  11. Mortad M.H., On some product of two unbounded self-adjoint operators, Integral Equations Operator Theory, 2009, 64/3, 399-408 Zbl1241.47018
  12. 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
  13. 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
  14. 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] 
  15. Mortad M.H., Products of Unbounded Normal Operators. arXiv:1202.6143v1 Zbl1262.47008
  16. Mortad M.H., The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness and Normality, (submitted). arXiv:1203.2545v1 Zbl1268.47002
  17. Patel A., Ramanujan P.B., On sum and product of normal operators, Indian J. Pure Appl. Math., 1981, 12/10, 1213-1218 Zbl0469.47019
  18. Rudin W., Functional analysis, McGraw-Hill, 1991 (2nd edition) Zbl0867.46001
  19. Weidmann J., Linear operators in Hilbert spaces, Springer, 1980 Zbl0434.47001
  20. Wiegmann N.A., Normal products of matrices, Duke Math J., 1948, 15, 633-638[Crossref][WoS] Zbl0031.24302
  21. Wiegmann N.A., A note on infinite normal matrices, Duke Math. J., 1949, 16, 535-538 Zbl0035.19702

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