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Abstrakty
Some inequalities for the maximum and the minimum of the spectrum for the real part of a product of two operators in Hilbert spaces are given. Applications for one operator whose transform C(...) (introduced by the author in [9]) is accretive, are given as well.
Wydawca
Czasopismo
Rocznik
Tom
Strony
665--680
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Mathematics, School of Engineering & Science Victoria University PO BOX 14428 Melbourne City, Vic, Australia 8001 http://rgmia.org/dragomir/, sever.dragomir@vu.edu.au
Bibliografia
- [1] F. F. Bonsall, J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Series, No. 2, Cambridge University Press, 1971.
- [2] F. F. Bonsall, J. Duncan, Numerical Ranges II , London Math. Soc. Lecture Notes Series, No. 10, Cambridge University Press, 1973.
- [3] S. S. Dragomir, Semi Inner Products and Applications, Nova Science Publishers Inc., N.Y., 2004.
- [4] S. S. Dragomir, Reverse inequalities for the numerical radius of linear operators in Hilbert spaces, Bull. Austral. Math. Soc. 73 (2006), 255–262.
- [5] S. S. Dragomir, Some inequalities for the Euclidean operator radius of two operators in Hilbert spaces, Linear Algebra Appl. 419(1) (2006), 256–264.
- [6] S. S. Dragomir, Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Demonstratio Math. 40 (2007), 411–417.
- [7] S. S. Dragomir, Inequalities for the norm and the numerical radius of composite operators in Hilbert spaces, Preprint available in RGMIA Res. Rep. Coll. 8 (2005), Supplement, Article 11 [on-line: http://rgmia.vu.edu.au/v8(E).html].
- [8] S. S. Dragomir, New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces, Linear Algebra Appl. 428 (2008), 2750–2760.
- [9] S. S. Dragomir, Inequalities for the numerical radius, the norm and the maximum of the real part of bounded linear operators in Hilber spaces, Linear Algebra Appl. 428 (2008), 2980–2994.
- [10] K. E. Gustafson, D. K. M. Rao, Numerical Range, Springer Verlag, New York, 1997.
- [11] P. R. Halmos, A Hilbert Space Problem Book, Second Ed., Springer-Verlag, New York, 1982.
- [12] F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 168(1) (2005), 73–80.
- [13] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math. 158(1) (2003), 11–17.
- [14] G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100(1) (1961), 29–43.
- [15] J. K. Merikoski, R. Kumar, Lower bounds for the numerical radius, Linear Algebra Appl. 410 (2005), 135–142.
- [16] G. Söderlind, The logarithmic norm. History and modern theory, BIT 46 (2006), 631–652.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-PWA4-0032-0024