Abstract:We demonstrate the result stated in the title, thus answering an open question asked by Julio Becerra Guerrero, Ginés López-Pérez and Abraham Rueda Zoca [J. Convex. Anal. 25, (2018), pp. 817–840].
- Antonio Avilés, Vladimir Kadets, Miguel Martín, Javier Merí, and Varvara Shepelska, Slicely countably determined Banach spaces, Trans. Amer. Math. Soc. 362 (2010), no. 9, 4871–4900. MR 2645054, DOI 10.1090/S0002-9947-10-05038-5
- Julio Becerra Guerrero, Ginés López-Pérez, and Abraham Rueda Zoca, Diametral diameter two properties in Banach spaces, J. Convex Anal. 25 (2018), no. 3, 817–840. MR 3818544, DOI 10.1017/s0308210517000373
- I. K. Daugavet, A property of completely continuous operators in the space $C$, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 157–158 (Russian). MR 0157225
- Rainis Haller, Katriin Pirk, and Märt Põldvere, Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm, Acta Comment. Univ. Tartu. Math. 20 (2016), no. 1, 101–105. MR 3521706, DOI 10.12697/ACUTM.2016.20.08
- Rainis Haller, Johann Langemets, and Rihhard Nadel, Stability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums, Banach J. Math. Anal. 12 (2018), no. 1, 222–239. MR 3745582, DOI 10.1215/17358787-2017-0040
- Y. Ivakhno, V. Kadets Unconditional sums of spaces with bad projections, Visn. Khark. Univ., Ser. Mat. Prykl. Mat. Mekh. 54 (2004), 30–35.
- V. Kadets, Banach spaces with the Daugavet property and Banach spaces with numerical index 1. Doctor of science thesis (in Russian). Kharkiv V. N. Karazin National University (2014), 307 pp. doi:10.13140/RG.2.1.2465.7689
- Vladimir M. Kadets, Roman V. Shvidkoy, Gleb G. Sirotkin, and Dirk Werner, Banach spaces with the Daugavet property, Trans. Amer. Math. Soc. 352 (2000), no. 2, 855–873. MR 1621757, DOI 10.1090/S0002-9947-99-02377-6
- Vladimir M. Kadets, Roman V. Shvidkoy, and Dirk Werner, Narrow operators and rich subspaces of Banach spaces with the Daugavet property, Studia Math. 147 (2001), no. 3, 269–298. MR 1853772, DOI 10.4064/sm147-3-5
- Vladimir Kadets, Miguel Martín, Javier Merí, and Antonio Pérez, Spear operators between Banach spaces, Lecture Notes in Mathematics, vol. 2205, Springer, Cham, 2018. MR 3753623, DOI 10.1007/978-3-319-71333-5
- R. Nadel, Big slices of the unit ball in Banach spaces, Dissertationes Mathematicae Universitatis Tartuensis 132, University of Tartu Press, 2020, 109 pp.
- K. Pirk, Diametral diameter two properties, Daugavet-, and $\Delta$-points in Banach spaces, Dissertationes Mathematicae Universitatis Tartuensis 133, University of Tartu Press, 2020, 106 pp.
- R. V. Shvydkoy, Geometric aspects of the Daugavet property, J. Funct. Anal. 176 (2000), no. 2, 198–212. MR 1784413, DOI 10.1006/jfan.2000.3626
- Vladimir Kadets
- Affiliation: School of Mathematics and Informatics, V. N. Karazin Kharkiv National University, 61022 Kharkiv, Ukraine
- MR Author ID: 202226
- ORCID: 0000-0002-5606-2679
- Email: firstname.lastname@example.org
- Received by editor(s): October 11, 2020
- Published electronically: March 22, 2021
- Additional Notes: The research was partially supported by project PGC2018-093794-B-I00 (MCIU/AEI/FEDER, UE), and on its final stage by National Research Foundation of Ukraine funded by Ukrainian State budget in frames of project 2020.02/0096 “Operators in infinite-dimensional spaces: the interplay between geometry, algebra and topology”.
- Communicated by: Stephen Dilworth
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 2579-2582
- MSC (2020): Primary 46B20
- DOI: https://doi.org/10.1090/proc/15448
- MathSciNet review: 4246808