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Approximate isosceles \(\omega \)-orthogonality and approximate \(\omega \)-parallelism

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Abstract

We introduce two notions of approximate isosceles \(\omega \)-orthogonality and two notions of approximate \(\omega \)-parallelism for bounded linear operators on a Hilbert space. Moreover, we state some basic properties of these notions and investigate some relations between them.

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References

  1. Amyari, M., Moradian Khibary, M.: Approximate \(\omega \)-orthogonality and \(\omega \)-derivation. Math. Inequal. Appl. 24(2), 463–476 (2021)

    MathSciNet  MATH  Google Scholar 

  2. Bhunia, P., Dragomir, S.S., Moslehian, M.S., Paul, K.: Lectures on Numerical Radius Inequalities, Infosys Science Foundation Series, Infosys Science Foundation Series in Mathematical Sciences. Springer, Cham (2022)

    Google Scholar 

  3. Bhunia, P., Feki, K., Paul, K.: \(A\)-numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications. Bull. Iran. Math. Soc. 47(2), 435–457 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bottazzi, T., Conde, C., Sain, D.: A study of orthogonality of bounded linear operators. Banach J. Math. Anal. 14(3), 1001–1018 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chmieliński, J.: On an \(\varepsilon \)-Birkhoff orthogonality, JIPAM. J. Inequal. Pure Appl. Math. 6(3) (2005). Article 79, 7 pp

  6. Hirzallah, O., Kittaneh, F., Shebrawi, K.: Numerical radius inequalities for certain \(2\times 2\) operator matrices. Integral Equ. Oper. Theory 71(1), 129–147 (2011)

    Article  MATH  Google Scholar 

  7. Mehrazin, M., Amyari, M., Zamani, A.: Numerical radius parallelism of Hilbert space operators. Bull. Iran. Math. Soc. 46(3), 821–829 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  8. Moslehian, M.S., Muñoz-Fernández, G.A., Peralta, A.M., Seoane-Sepúlveda, J.B.: Similarities and differences between real and complex Banach spaces: an overview and recent developments. Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM 116(2) (2022). Paper No. 88, 80 pp

  9. Paul, K., Bag, S.: On numerical radius of a matrix and estimation of bounds for zeros of a polynomial, Int. J. Math. Math. Sci. (2012). Art. ID 129132, 15 pp

  10. Rooin, J., Karami, S., Ghaderi Aghideh, M.: A new approach to numerical radius of quadratic operators. Ann. Funct. Anal. 11(3), 879–896 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  11. Seddik, A.: Rank one operators and norm of elementary operators. Linear Algebra Appl. 424, 177–183 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sen, J., Sain, D., Paul, K.: Orthogonality and norm attainment of operators in semi-Hilbertian spaces. Ann. Funct. Anal. 12(1) (2021). Paper No. 17, 12 pp

  13. Torabian, M., Amyari, M., Moradian Khibary, M.: More on \(\omega \)-orthogonalities and \(\omega \)-parallelism. Linear Multilinear Algebra 70(14), 2619–2628 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zamani, A., Moslehian, M.S.: Exact and approximate operator parallelism. Canad. Math. Bull. 58(1), 207–224 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zamani, A., Wójcik, P.: Numerical radius orthogonality in \(C^*\)-algebras. Ann. Funct. Anal. 11(4), 1081–1092 (2020)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the reviewer for valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    M. Amyari & M. Torabian

  2. Department of Mathematics, Farhangian University, Mashhad, Iran

    M. Moradian Khibary

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  1. M. Amyari
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  2. M. Torabian
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  3. M. Moradian Khibary
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Correspondence to M. Amyari.

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Amyari, M., Torabian, M. & Moradian Khibary, M. Approximate isosceles \(\omega \)-orthogonality and approximate \(\omega \)-parallelism. Bol. Soc. Mat. Mex. 29, 59 (2023). https://doi.org/10.1007/s40590-023-00528-w

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  • DOI: https://doi.org/10.1007/s40590-023-00528-w

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