Absolutely minimum attaining Toeplitz and absolutely norm attaining Hankel operators

Golla Ramesh; Shanola S. Sequeira

doi:10.5802/crmath.457

Théorie des opérateurs

Absolutely minimum attaining Toeplitz and absolutely norm attaining Hankel operators

Golla Ramesh ¹ ; Shanola S. Sequeira ¹

¹ Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Telangana-502284, India

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 973-977.

Résumé

In this article, we completely characterize absolutely norm attaining Hankel operators and absolutely minimum attaining Toeplitz operators. We also improve [19, Theorem 2.1], by characterizing the absolutely norm attaining Toeplitz operator $T_{φ}$ in terms of the symbol $φ \in L^{\infty}$ .

Reçu le : 2022-10-13
Révisé le : 2022-11-04
Accepté le : 2022-12-18
Publié le : 2023-09-07

DOI : 10.5802/crmath.457

Classification : 47B35, 47A10, 47B07

Affiliations des auteurs :

Golla Ramesh ¹ ; Shanola S. Sequeira ¹

¹ Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Telangana-502284, India

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Golla Ramesh and Shanola S. Sequeira},
     title = {Absolutely minimum attaining {Toeplitz} and absolutely norm attaining {Hankel} operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {973--977},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.457},
     language = {en},
}

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Golla Ramesh; Shanola S. Sequeira. Absolutely minimum attaining Toeplitz and absolutely norm attaining Hankel operators. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 973-977. doi : 10.5802/crmath.457. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.457/

Bibliographie
Cité par

[1] María D. Acosta; Richard M. Aron; Domingo García; Manuel Maestre The Bishop-Phelps-Bollobás theorem for operators, J. Funct. Anal., Volume 254 (2008) no. 11, pp. 2780-2799 | DOI | Zbl

[2] Errett Bishop; Robert R. Phelps A proof that every Banach space is subreflexive, Bull. Am. Math. Soc., Volume 67 (1961), pp. 97-98 | DOI | MR | Zbl

[3] Arlen Brown; Ronald G. Douglas Partially isometric Toeplitz operators, Proc. Am. Math. Soc., Volume 16 (1965), pp. 681-682 | DOI | MR | Zbl

[4] Arlen Brown; Paul R. Halmos Algebraic properties of Toeplitz operators, J. Reine Angew. Math., Volume 213 (1963), pp. 89-102 | MR | Zbl

[5] Xavier Carvajal; Wladimir Neves Operators that achieve the norm, Integral Equations Oper. Theory, Volume 72 (2012) no. 2, pp. 179-195 | DOI | MR | Zbl

[6] Xavier Carvajal; Wladimir Neves Operators that attain their minima, Bull. Braz. Math. Soc. (N.S.), Volume 45 (2014) no. 2, pp. 293-312 | DOI | MR | Zbl

[7] Ronald G. Douglas Banach algebra techniques in operator theory, Graduate Texts in Mathematics, 179, Springer, 1998 | DOI

[8] Per Enflo; Janice Kover; Laura Smithies Denseness for norm attaining operator-valued functions, Linear Algebra Appl., Volume 338 (2001) no. 1-3, pp. 139-144 | DOI | MR | Zbl

[9] Jadav Ganesh; Gola Ramesh; Daniel Sukumar A characterization of absolutely minimum attaining operators, J. Math. Anal. Appl., Volume 468 (2018) no. 1, pp. 567-583 | MR

[10] Philip Hartman On completely continuous Hankel matrices, Proc. Am. Math. Soc., Volume 9 (1958), pp. 862-866 | DOI | MR | Zbl

[11] Janice Kover Compact perturbations and norm attaining operators, Quaest. Math., Volume 28 (2005) no. 4, pp. 401-408 | DOI | MR | Zbl

[12] Joram Lindenstrauss On operators which attain their norm, Isr. J. Math., Volume 1 (1963), pp. 139-148 | DOI | MR | Zbl

[13] Rubén A. Martínez-Avendaño; Peter Rosenthal An introduction to operators on the Hardy–Hilbert space, Graduate Texts in Mathematics, 237, Springer, 2007

[14] D. Venku Naidu; Golla Ramesh On absolutely norm attaining operators, Proc. Indian Acad. Sci., Math. Sci., Volume 129 (2019) no. 4, 54, 17 pages | MR | Zbl

[15] Bala Neeru; Golla Ramesh Spectral properties of absolutely minimum attaining operators, Banach J. Math. Anal., Volume 14 (2020) no. 3, pp. 630-649 | DOI | MR | Zbl

[16] Satish K. Pandey; Vern I. Paulsen A spectral characterization of $𝒜𝒩$ operators, J. Aust. Math. Soc., Volume 102 (2017) no. 3, pp. 369-391 | DOI | Zbl

[17] Vladimir V. Peller Hankel operators and their applications, Springer Monographs in Mathematics, Springer, 2003 | DOI | MR

[18] Golla Ramesh Absolutely norm attaining paranormal operators, J. Math. Anal. Appl., Volume 465 (2018) no. 1, pp. 547-556 | DOI | MR | Zbl

[19] Golla Ramesh; Shanola S. Sequeira Absolutely norm attaining Toeplitz and absolutely minimum attaining Hankel operators, J. Math. Anal. Appl., Volume 516 (2022) no. 1, 126497, 12 pages | MR | Zbl

[20] Golla Ramesh; Shanola S. Sequeira On the closure of absolutely norm attaining operators (2022) (to appear in Linear Multilinear Algebra, https://doi.org/10.1080/03081087.2022.2126426)

[21] Takashi Yoshino The structure of norm-achieved Toeplitz and Hankel operators, Nihonkai Math. J., Volume 13 (2002) no. 1, pp. 43-55 | MR | Zbl

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