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Parameters in Banach spaces and orthogonality

Year 2022, , 37 - 45, 14.03.2022
https://doi.org/10.33205/cma.1067323

Abstract

In Banach spaces, plenty of parameters have been considered: they are often defined by using
pairs of vectors. Rarely, they are defined by considering pairs of vectors which are orthogonal in
the sense of Birkhoff and James; in that case the study is often not easy. In fact, it can be difficult
to identify pairs of orthogonal vectors; so to calculate the value of these parameters, to compare
them with the other parameters, to see if they have some stability with respect to changes of the
norm. In this paper, we shall do this for a couple of new parameters.

References

  • J. Alonso, H. Martini and S. Wu: On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces, Aequationes Math., 83 (1-2) (2012), 153–189.
  • M. Baronti, E. Casini and P. L. Papini: Revisiting the rectangular constant in Banach spaces, Bull. Aust. Math. Soc., 105 (1) (2022), 124–133.
  • E. Casini: About some parameters of normed linear spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., 80 (1986), 11–15.
  • M. Kato, L. Maligranda and Y. Takahashi: On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces, Studia Math., 144 (3) (2001), 275–295.
  • P. L. Papini: Constants and symmetries in Banach spaces, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 56 (2002), 65–76.
  • I. Şerb: On a modified modulus of smoothness of a Banach space, Rev. Anal. Numér. Théor. Approx., 22 (2) (1993), 217–224.
  • C. S. Yang, H. Y. Li: The James constant for the $\ell_3 - \ell_1$ space, Acta Math. Sin. (Engl. Ser.), 32 (9) (2016), 1075–1079.
Year 2022, , 37 - 45, 14.03.2022
https://doi.org/10.33205/cma.1067323

Abstract

References

  • J. Alonso, H. Martini and S. Wu: On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces, Aequationes Math., 83 (1-2) (2012), 153–189.
  • M. Baronti, E. Casini and P. L. Papini: Revisiting the rectangular constant in Banach spaces, Bull. Aust. Math. Soc., 105 (1) (2022), 124–133.
  • E. Casini: About some parameters of normed linear spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., 80 (1986), 11–15.
  • M. Kato, L. Maligranda and Y. Takahashi: On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces, Studia Math., 144 (3) (2001), 275–295.
  • P. L. Papini: Constants and symmetries in Banach spaces, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 56 (2002), 65–76.
  • I. Şerb: On a modified modulus of smoothness of a Banach space, Rev. Anal. Numér. Théor. Approx., 22 (2) (1993), 217–224.
  • C. S. Yang, H. Y. Li: The James constant for the $\ell_3 - \ell_1$ space, Acta Math. Sin. (Engl. Ser.), 32 (9) (2016), 1075–1079.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Pier Luigi Papini 0000-0002-2337-7906

Marco Barontı 0000-0001-8827-4855

Publication Date March 14, 2022
Published in Issue Year 2022

Cite

APA Papini, P. L., & Barontı, M. (2022). Parameters in Banach spaces and orthogonality. Constructive Mathematical Analysis, 5(1), 37-45. https://doi.org/10.33205/cma.1067323
AMA Papini PL, Barontı M. Parameters in Banach spaces and orthogonality. CMA. March 2022;5(1):37-45. doi:10.33205/cma.1067323
Chicago Papini, Pier Luigi, and Marco Barontı. “Parameters in Banach Spaces and Orthogonality”. Constructive Mathematical Analysis 5, no. 1 (March 2022): 37-45. https://doi.org/10.33205/cma.1067323.
EndNote Papini PL, Barontı M (March 1, 2022) Parameters in Banach spaces and orthogonality. Constructive Mathematical Analysis 5 1 37–45.
IEEE P. L. Papini and M. Barontı, “Parameters in Banach spaces and orthogonality”, CMA, vol. 5, no. 1, pp. 37–45, 2022, doi: 10.33205/cma.1067323.
ISNAD Papini, Pier Luigi - Barontı, Marco. “Parameters in Banach Spaces and Orthogonality”. Constructive Mathematical Analysis 5/1 (March 2022), 37-45. https://doi.org/10.33205/cma.1067323.
JAMA Papini PL, Barontı M. Parameters in Banach spaces and orthogonality. CMA. 2022;5:37–45.
MLA Papini, Pier Luigi and Marco Barontı. “Parameters in Banach Spaces and Orthogonality”. Constructive Mathematical Analysis, vol. 5, no. 1, 2022, pp. 37-45, doi:10.33205/cma.1067323.
Vancouver Papini PL, Barontı M. Parameters in Banach spaces and orthogonality. CMA. 2022;5(1):37-45.