Skip to main content
SpringerLink
Log in

Inequalities for Two Operators

  • Chapter
  • First Online:
Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

Abstract

In this chapter we present recent results obtained by the author concerning the norms and the numerical radii of two bounded linear operators. The proofs of the results are elementary. Some vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dragomir, S.S.: A generalisation of Grüss’ inequality in inner product spaces and applications. J. Math. Anal. Applic. 237, 74–82 (1999)

    Article  MATH  Google Scholar 

  2. Dragomir, S.S.: Some Grüss type inequalities in inner product spaces. J. Inequal. Pure & Appl. Math. 4(2), Article 42 (2003)

    Google Scholar 

  3. Dragomir, S.S.: New reverses of Schwarz, triangle and Bessel inequalities in inner product spaces. Australian J. Math. Anal. & Appl. 1(1), Article 1, 1–18 (2004)

    Google Scholar 

  4. Dragomir, S.S.: Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces. J. Inequal. Pure & Appl. Math., 5(3), Article 76 (2004)

    Google Scholar 

  5. Dragomir, S.S.: A counterpart of Schwarz’s inequality in inner product spaces. East Asian Math. J. 20(1), 1–10 (2004)

    MATH  Google Scholar 

  6. Dragomir, S.S.: Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., New York (2005)

    Google Scholar 

  7. Dragomir, S.S.: Inequalities for the norm and the numerical radius of composite operators in Hilbert spaces. Inequalities and applications. Internat. Ser. Numer. Math. 157, 135–146 Birkhäuser, Basel, 2009. Preprint available in RGMIA Res. Rep. Coll. 8 (2005), Supplement, Article 11

    Google Scholar 

  8. Dragomir, S.S.: Some inequalities for the Euclidean operator radius of two operators in Hilbert spaces. Linear Algebra Appl. 419(1), 256–264 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dragomir, S.S.: Reverse inequalities for the numerical radius of linear operators in Hilbert spaces. Bull. Austral. Math. Soc. 73(2), 255–262 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dragomir, S.S.: Reverses of the Schwarz inequality generalising a Klamkin-McLenaghan result. Bull. Austral. Math. Soc.73(1), 69–78 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dragomir, S.S.: Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces. Demonstratio Math. 40(2), 411–417 (2007)

    MathSciNet  MATH  Google Scholar 

  12. Dragomir, S.S.: Norm and numerical radius inequalities for a product of two linear operators in Hilbert spaces. J. Math. Inequal. 2(4), 499–510 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dragomir, S.S.: New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces. Linear Algebra Appl. 428(11–12), 2750–2760 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dragomir, S.S.: Some inequalities of the Grüss type for the numerical radius of bounded linear operators in Hilbert spaces. J. Inequal. Appl. 2008, Art. ID 763102, 9 pp. Preprint, RGMIA Res. Rep. Coll. 11(1) (2008)

    Google Scholar 

  15. Dragomir, S.S.: Some inequalities for commutators of bounded linear operators in Hilbert spaces, Preprint. RGMIA Res. Rep. Coll.11(1), Article 7 (2008)

    Google Scholar 

  16. Dragomir, S.S.: Power inequalities for the numerical radius of a product of two operators in Hilbert spaces.Sarajevo J. Math. 5(18)(2), 269–278 (2009)

    Google Scholar 

  17. Dragomir, S.S.: A functional associated with two bounded linear operators in Hilbert spaces and related inequalities. Ital. J. Pure Appl. Math. No. 27, 225–240 (2010)

    MATH  Google Scholar 

  18. Dragomir, S.S., SÁNDOR, J.: Some inequalities in prehilbertian spaces. Studia Univ. “Babeş-Bolyai” - Mathematica 32(1), 71–78 (1987)

    Google Scholar 

  19. Goldstein, A., Ryff, J.V., Clarke, L.E.: Problem 5473. Amer. Math. Monthly 75(3), 309 (1968)

    Article  MathSciNet  Google Scholar 

  20. Gustafson, K.E., Rao, D.K.M. Numerical Range Springer, New York, Inc. (1997)

    Book  Google Scholar 

  21. Halmos, P.R.: A Hilbert Space Problem Book, 2nd edn. Springer-Verlag, New York, Heidelberg, Berlin (1982)

    Book  MATH  Google Scholar 

  22. Kittaneh, F.: Notes on some inequalities for Hilbert space operators. Publ. Res. Inst. Math. Sci. 24, 283–293 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kittaneh, F.: A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix. Studia Math. 158(1), 11–17 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kittaneh, F.: Numerical radius inequalities for Hilbert space operators. Studia Math. 168(1), 73–80 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pearcy, C.: An elementary proof of the power inequality for the numerical radius. Michigan Math. J. 13, 289–291 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  26. Popescu, G.: Unitary invariants in multivariable operator theory. Mem. Amer. Math. Soc. 200(941), vi+91 (2009) ISBN: 978-0-8218-4396-3. Preprint, Arχiv.math.OA/0410492

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Engineering and Science, Victoria University, Melbourne, Australia

    Silvestru Sever Dragomir

  2. School of Computational and Applied Mathematics, University of the Withwatersrand Braamfontein, Johannesburg, South Africa

    Silvestru Sever Dragomir

Authors
  1. Silvestru Sever Dragomir
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Silvestru Sever Dragomir

About this chapter

Cite this chapter

Dragomir, S.S. (2013). Inequalities for Two Operators. In: Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-01448-7_3

Download citation

Publish with us

Policies and ethics

Search

Navigation