논문KCI 등재
Extension of phase-isometries between the unit spheres of atomic $L_p$-spaces for $p>0$
대한수학회 (The Korean Mathematical Society)|2019.11|대한수학회보 (Bulletin of the KMS)|제56권 제6호|pp. 1377-1384|DOI 10.4134/BKMS.b180561
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper, we prove that for every surjective phase-iso\-metry between the unit spheres of real atomic $L_p$-spaces for $p>0$, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.
Abstract
In this paper, we prove that for every surjective phase-iso\-metry between the unit spheres of real atomic $L_p$-spaces for $p>0$, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.
참고문헌 (13)
- D. F. Almeida, "The rst mathematical proof of Wigner's theorem", J. Natur. Geom, 2(2), pp.113~123 (1992)
- S. Banach, "Theorie des operations lineaires" (1993), Editions Jacques Gabay
- GuangGui Ding, "On isometric extension problem between two unit spheres", Science in China Series A: Mathematics, 52(10), pp.2069~2083 (2009), Springer Science and Business Media LLC[DOI]
- Gy.P. Gehér, "An elementary proof for the non-bijective version of Wigner's theorem", Physics Letters A, 378(30-31), pp.2054~2057 (2014), Elsevier BV[DOI]
- MáTé Győry, "A new proof of Wigner's theorem", Reports on Mathematical Physics, 54(2), pp.159~167 (2004), Elsevier BV[DOI]
- Xujian Huang, "Wigner's theorem in atomic $L_p$-spaces ($p>0$)", Publicationes Mathematicae Debrecen, 92(3-4), pp.411~418 (2018), University of Debrecen[DOI]
- J. Lamperti, "On the isometries of certain function-spaces", Pacic J. Math, 8, pp.459~466 (1958)[DOI]
- Lajos Molnár, "Orthogonality Preserving Transformations on Indefinite Inner Product Spaces: Generalization of Uhlhorn's Version of Wigner's Theorem", Journal of Functional Analysis, 194(2), pp.248~262 (2002), Elsevier BV[DOI]
- A. M. Peralta, "The Mazur-Ulam property for commutative von Neumann algebras, Linear and Multilinear A", arXiv:1803.00604, ~ (2018)
- Jürg Rätz, "On Wigner's theorem: Remarks, complements, comments, and corollaries", Aequationes Mathematicae, 52(1), pp.1~9 (1996), Springer Science and Business Media LLC[DOI]
- Daryl Tingley, "Isometries of the unit sphere", Geometriae Dedicata, 22(3), pp.371~378 (1987), Springer Science and Business Media LLC[DOI]
- A. Turnsek, "A variant of Wigner's functional equation", Aequationes Math, 89(4), pp.1~8 (2015)
- J. Wang, "On extension of isometries between unit spheres of ALp-spaces (0 < p < 1)", Proc. Amer. Math. Soc., 132(10), pp.2899~2909 (2004)
관련 논문AI추천
Extreme points of the space ${\mathcal L}(^2l_{\infty})$김성권대한수학회 · 대한수학회논문집2020 · 제35권 제3호Smooth points of ${\mathcal L}_s(^nl_{\infty}^2)$김성권대한수학회 · 대한수학회보2020 · 제57권 제2호Generalizations of Alesandrov problem and Mazur-Ulam theorem for two-isometries and two-expansive mappingsAbdulqader Mohammadi, Hamid Khodaei대한수학회 · 대한수학회논문집2019 · 제34권 제3호Liftings of absolutely summing operators on $\mathcal{L}_1^\lambda-$ spaces강정흥강원경기수학회 · 한국수학논문집2022 · 제30권 제1호Extreme points of the closed unit ball of $\qk0$ spacesHasi Wulan, Tiantian Chen대한수학회 · 대한수학회보2025 · 제62권 제5호The Aleksandrov problem and the Mazur-Ulam theorem on linear n-normed spacesMa Yumei대한수학회 · 대한수학회보2013 · 제50권 제5호
이 간행물의 다른 논문 (17건)
Negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$Jirayu Phuto, Chakkrid Klin-eampp. 1385-1422Riemann-Liouville fractional fundamental theorem of calculus and Riemann-Liouville fractional Polya type integral inequality and its extension to Choquet integral settingGeorge A. Anastassioupp. 1423-1433Reliability analysis of checkpointing model with multiple verification mechanism이유태pp. 1435-1445Mild solutions for the relativistic Vlasov-Klein-Gordon systemXianwen Zhang, Meixia Xiaopp. 1447-1465Robust optimal proportional reinsurance and investment strategy for an insurer with Ornstein-Uhlenbeck processYongsheng Xing, Guojing Wang, Jianjing Mapp. 1467-1483