Hermitian Forms and Inequalities for Sequences and Power Series of Operators in Hilbert Spaces

Dragomir, S. S.

doi:10.1515/awutm-2017-0005

Abstract

By the use of some inequalities for nonnegative Hermitian forms various inequalities for sequences and power series of bounded linear operators in complex Hilbert spaces are established. Applications for some fundamental functions of interest are also given.

References

[1] N. G. de Bruijn, Problem 12, Wisk. Opgaven, 21, (1960), 12-14.10.1080/00031305.1960.10501685
Search in Google Scholar Back to article
[2] M. L. Buzano, Generalizzazione della diseguaglianza di Cauchy-Schwarz. (Italian), Rend. Sem. Mat. Univ. e Politech. Torino, 31, (1974), 405-409.
Search in Google Scholar Back to article
[3] S. S. Dragomir, Some refinements of Schwartz inequality, Simpozionul de Matematici şi Aplicaţii, Timişoara, Romania, 1-2 Noiembrie 1985, 13-16.
Search in Google Scholar Back to article
[4] S. S. Dragomir, Grüss inequality in inner product spaces, The Australian Math Soc. Gazette, 26, (1999), 66-70.
Search in Google Scholar Back to article
[5] S. S. Dragomir, A generalization of Grüss' inequality in inner product spaces and applications, J. Math. Anal. Appl., 237, (1999), 74-82.10.1006/jmaa.1999.6452
Search in Google Scholar Back to article
[6] S. S. Dragomir, Some Grüss type inequalities in inner product spaces, J. Inequal. Pure & Appl. Math., 4, (2003), Article 42. (Online http://jipam.vu.edu.au/article.php?sid=280).
Search in Google Scholar Back to article
[7] S. S. Dragomir, Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces, J. Inequal. Pure & Appl. Math., 5, (2004), Article 76. (Online : http://jipam.vu.edu.au/article.php?sid=432).
Search in Google Scholar Back to article
[8] S. S. Dragomir, New reverses of Schwarz, triangle and Bessel inequalities in inner product spaces, Austral. J. Math. Anal. & Applics., 1, (2004), Article 1. (Online: http://ajmaa.org/cgi-bin/paper.pl?string=nrstbiips.tex).
Search in Google Scholar Back to article
[9] S. S. Dragomir, On Bessel and Grüss inequalities for orthornormal families in inner product spaces, Bull. Austral. Math. Soc., 69, (2004), 327-340.10.1017/S0004972700036066
Search in Google Scholar Back to article
[10] S. S. Dragomir, Advances in Inequalities of the Schwarz, Grüss and Bessel Type in Inner Product Spaces, Nova Science Publishers Inc, New York,x+249 p., 2005.
Search in Google Scholar Back to article
[11] S. S. Dragomir, Reverses of the Schwarz inequality in inner product spaces generalising a Klamkin-McLenaghan result, Bull. Austral. Math. Soc., 73, (2006), 69-78.10.1017/S0004972700038636
Search in Google Scholar Back to article
[12] S. S. Dragomir, Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces., Nova Science Publishers, Inc., New York,xii+243 pp. ISBN: 978-1-59454-903-8; 1-59454-903-6 (Preprint http://rgmia.org/monographs/advancees2.htm), 2007.
Search in Google Scholar Back to article
[13] S. S. Dragomir, Some new Grüss' type inequalities for functions of selfadjoint operators in Hilbert spaces, Sarajevo J. Math., 6, (2010), 89107.10.1155/2010/496821
Search in Google Scholar Back to article
[14] S. S. Dragomir, Inequalities for the Čebyşev functional of two functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll., 11(e), (2008), Art. 17.
Search in Google Scholar Back to article
[15] S. S. Dragomir, Some inequalities for the Čebyşev functional of two functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll., 11(e), (2008), Art.8.
Search in Google Scholar Back to article
[16] S. S. Dragomir, Inequalities for the Čebyşev functional of two functions of selfadjoint operators in Hilbert spaces, Aust. J. Math. Anal. & Appl., 6, (2009), Article 7, pp. 1-58.
Search in Google Scholar Back to article
[17] S. S. Dragomir, Some inequalities for power series of selfadjoint operators in Hilbert spaces via reverses of the Schwarz inequality, Integral Transforms Spec. Funct., 20, (2009), 757-76710.1080/10652460902910054
Search in Google Scholar Back to article
[18] S. S. Dragomir, Operator Inequalities of the Jensen, Čebyşev and Grüss Type, Springer Briefs in Mathematics. Springer, New York, xii+121 pp. ISBN: 978-1-4614- 1520-6, 2012.10.1007/978-1-4614-1521-3_3
Search in Google Scholar Back to article
[19] S. S. Dragomir, Operator Inequalities of Ostrowski and Trapezoidal Type, Springer Briefs in Mathematics. Springer, New York, x+112 pp. ISBN: 978-1-4614-1778-1, 2012.10.1007/978-1-4614-1779-8_3
Search in Google Scholar Back to article
[20] S. S. Dragomir, Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces, Springer Briefs in Mathematics. Springer, x+120 pp. ISBN: 978-3-319-01447-0; 978-3-319-01448-7, 2013.
Search in Google Scholar Back to article
[21] S. S. Dragomir, M. V. Boldea, C. Buşe, and M. Megan, Norm inequalities of Čebyşev type for power series in Banach algebras, J. Inequal. Appl., 2014:294, (2014), 19 pp.10.1186/1029-242X-2014-294
Search in Google Scholar Back to article
[22] S. S. Dragomir and B. Mond, On the superadditivity and monotonicity of Schwarz's inequality in inner product spaces, Contributions, Macedonian Acad. of Sci and Arts, 15, (1994), 5-22.
Search in Google Scholar Back to article
[23] S. S. Dragomir and B. Mond, Some inequalities for Fourier coefficients in inner product spaces, Periodica Math. Hungarica, 32, (1995), 167-172.10.1007/BF01882192
Search in Google Scholar Back to article
[24] S. S. Dragomir, J. Pečarič, and J. Şandor, The Chebyshev inequality in pre- Hilbertian spaces. II., Proceedings of the Third Symposium of Mathematics and its Applications (Timişoara, 1989), (1990), 75-78.
Search in Google Scholar Back to article
[25] S. S. Dragomir and J. Şandor, The Chebyshev inequality in pre-Hilbertian spaces. I., Proceedings of the Second Symposium of Mathematics and its Applications (Timişoara, 1987), (1988.), 61-64.
Search in Google Scholar Back to article
[26] K. E. Gustafson and D. K. M. Rao, Numerical Range, Springer-Verlag, New York, Inc., 1997.10.1007/978-1-4613-8498-4
Search in Google Scholar Back to article
[27] S. Kurepa, Note on inequalities associated with Hermitian functionals, Glasnik Matemaţcki, 3, (1968), 196-205.
Search in Google Scholar Back to article

Hermitian Forms and Inequalities for Sequences and Power Series of Operators in Hilbert Spaces

Abstract

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