On the Normality of the Unbounded Product of Two Normal Operators

• Autorzy: Mohammed Hichem Mortad
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Unbounded Operators; Normal Operators; Fuglede-Putnam Theorem

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 47B25: Symmetric and selfadjoint operators (unbounded)

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2013
• Tom: 1
• Strony: 11-18

Daty

online

2012-10-23

Twórcy

autor

Mohammed Hichem Mortad

• Department of Mathematics, University of Oran, B.P. 1524, El Menouar, Oran 31000, Algeria

Bibliografia

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

Identyfikatory

DOI

10.2478/conop-2012-0002