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On Bessel and Grüss inequalities for orthonormal families in inner product spaces

Published online by Cambridge University Press:  17 April 2009

S. S. Dragomir
S. S. Dragomir
Affiliation:
School of Computer Science and Mathematics, Victoria University of Technology, PO Box 14428, MCMC 8001 Victoria, Australia e-mail [email protected], urladdrhttp://rgmia.vu.edu.au/SSDragomirWeb.html
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A new reverse of Bessel's inequality for orthornormal families in real or complex inner product space is obtained. Applications for some Grüss type results are also provided.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 327 - 340
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Dragomir, S.S., ‘A generalisation of Grüss’ inequality in inner product spaces and applications’, J. Math. Anal. Appl. 237 (1999), 74–82.CrossRefGoogle Scholar
[2]Dragomir, S.S., ‘Some Grüss’ type inequalities in inner product spaces’, J. Ineq. Pure Appl. Math. 4 (2003), 10. Article 42 [ONLINE http://jipam.vu.edu.au/v4n2/032_03.html].Google Scholar
[3]Dragomir, S.S., ‘A counterpart of Bessel's inequality in inner product spaces and some Grüss type related results’, RGMIA Res. Rep. Coll. 6 (2003). Supplement, Article 10 [ONLINE http://rgmia.vu.edu.au/v6(E).html].Google Scholar
[4]Ujević, N., A new generalisation of Grüss inequality in inner product spaces, Math. Ineq. Appl. 6 (2003), 617–623.Google Scholar