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Abstrakty
We are mainly concerned with the result of Kaplansky on the composition of two normal operators in the case in which at least one of the operators is unbounded.
Wydawca
Rocznik
Tom
Strony
181--186
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Department of Mathematics University of Oran B.P. 1524, El Menouar Oran 31000, Algeria
autor
- Department of Mathematics University of Oran B.P. 1524, El Menouar Oran 31000, Algeria
Bibliografia
- [1] T. Ando, Operators with a norm condition, Acta Sci. Math. (Szeged) 33 (1972), 169–178.
- [2] S. K. Berberian, Introduction to Hilbert Space, reprint of the 1961 original, Chelsea, New York, 1976.
- [3] J. B. Conway, A Course in Functional Analysis, 2nd ed., Springer, 1990.
- [4] J. B. Conway, The Theory of Subnormal Operators, Math. Surveys Monogr. 36, Amer. Math. Soc., Providence, RI, 1991.
- [5] A. Devinatz, A. E. Nussbaum and J. von Neumann, On the permutability of selfadjoint operators, Ann. of Math. (2) 62 (1955), 199–203.
- [6] A. Gheondea, When are the products of normal operators normal?, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 52 (100) (2009), 129–150.
- [7] I. Gohberg, S. Goldberg and M. A. Kaashoek, Basic Classes of Linear Operators, Birkhäuser, Basel, 2003.
- [8] P. R. Halmos, A Hilbert Space Problem Book, 2nd ed., Springer, 1982.
- [9] Z. J. Jabłonski, I. B. Jung and J. Stochel, Unbounded quasinormal operators revisited, Integral Equations Operator Theory 79 (2014), 135–149.
- [10] I. Kaplansky, Products of normal operators, Duke Math. J. 20 (1953), 257–260.
- [11] F. Kittaneh, On the normality of operator products, Linear Multilinear Algebra 30 (1991) 1–4.
- [12] M. Martin and M. Putinar, Lectures on Hyponormal Operators, Operator Theory Adv. Appl. 39, Birkhäuser, Basel, 1989.
- [13] M. H. Mortad, On the closedness, the self-adjointness and the normality of the product of two unbounded operators, Demonstratio Math. 45 (2012), 161–167.
- [14] M. H. Mortad, Commutativity of unbounded normal and self-adjoint operators and applications, Operators and Matrices 8 (2014), 563–571.
- [15] A. B. Patel and P. B. Ramanujan, On sum and product of normal operators, Indian J. Pure Appl. Math. 12 (1981), 1213–1218.
- [16] W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill, 1991.
- [17] K. Schmüdgen, Unbounded Self-Adjoint Operators on Hilbert Space, Grad. Texts Math. 265, Springer, 2012.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-7f32642b-472a-4208-b035-953206c3c82b