EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp（Γ）（p〉1） SPACES

EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp（Γ）（p〉1） SPACES

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp（Γ） and lp（△）（p 〉1）. We first derive the representation of isometries between the unit spheres of complex Banach spaces lp（Γ） and lp（△）. Then we arrive at a conclusion that any surjective isometry...

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Veröffentlicht in:数学物理学报：B辑英文版 2014 (5), p.1540-1550
1. Verfasser: 伊继金 王瑞东 王晓晓
Format: Artikel
Sprache:eng
Schlagworte:
Banach空间
Pgt
单位球面
可扩展
满射
球面等距
线性等距
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Zusammenfassung:In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp（Γ） and lp（△）（p 〉1）. We first derive the representation of isometries between the unit spheres of complex Banach spaces lp（Γ） and lp（△）. Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces lp（Γ）and lp（△） can be extended to be a linear isometry on the whole space.
ISSN:0252-9602
1572-9087