Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces

• Autorzy: Dragomir S.
• Języki publikacji: EN

Abstrakty

EN

In this paper various inequalities between the operator norm and its numerical radius are provided. For this purpose, we employ some classical inequalities for vectors in inner product spaces due to Buzano, Goldstein-Ryff-Clarke, Dragomir-Sandor and the author.

Słowa kluczowe

EN

numerical range; numerical radius; bounded linear operators; Hilbert space

PL

numeryczny zbiór wartości; promień numeryczny; ograniczone operatory linearne; przestrzeń Hilberta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 2
• Strony: 411--417
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Dragomir S.

• School of Computer Science and Mathematics Victoria University PO Box 14428, Melbourne City Victoria 8001, Australia,

Bibliografia

• [1] M. L. Buzano, Generalizzazione della disiguaglianza di Cauchy-Schwaz (Italian), Rend. Sem. Mat. Univ. e Politech. Torino, 31 (1971/73), 405-409 (1974).
• [2] S. S. Dragomir, Some refinements of Schwarz inequality, Simposional de Matematică şi Aplicaţii, Polytechnical Institute Timişoara, Romania, 1-2 Nov., 1985, 13-16. ZBL 0594:46018.
• [3] S. S. Dragomir, Some Grüss type inequalities in inner product spaces, J. Ineq. Pure & Appl. Math. 4(2) (2003), Art. 42 (http://jipam.vu.edu.au/article.php?sid=280).
• [4] S. S. Dragomir, A potpourri of Schwarz related inequalities in inner product spaces (I), J. Ineq. Pure & Appl. Math. 6(3) (2005), Art. 59; http://jipam.vu.edu.au/article. php?sid=532.
• [5] S. S. Dragomir, A potpourri of Schwarz related inequalities in inner product spaces (II), J. Ineq. Pure & Appl. Math. 7(1) (2006), Art. 14; http://jipam.vu.edu.au/article.php?sid=619.
• [6] S. S. Dragomir, Reverse inequalities for the numerical radius of linear operators in Hilbert spaces, Bull. Austral. Math. Soc. 73 (2006), 255-262; online: RGMIA Res.Rep. Coll. 8 (2005), Article 9; http://rgmia.vu.edu.au/v8(E).html.
• [7] S. S. Dragomir and J. Sandor, Some inequalities in prehilbertian spaces, Studia Univ. "Babe¸s-Bolyai" - Mathematica 32(1) (1987), 71-78.
• [8] A. Goldstein, J. V. Ryff and L. E. Clarke, Problem 5473, Amer. Math. Monthly 75 (3) (1968), 309.
• [9] K. E. Gustaf son and D. K. M. Rao, Numerical Range, Springer-Verlag, New York, Inc., 1997.