Phase-isometries between two ℓp(Γ,H)-type spaces

Let Γ , Δ be nonempty index sets, and let H ,  K be inner product spaces. We prove that for p ≥ 1 any surjective phase-isometry between ℓ p ( Γ , H ) and ℓ p ( Δ , K ) is a plus–minus linear isometry. This can be considered as an extension of Wigner’s theorem for real ℓ p ( Γ , H ) -type spaces....

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Bibliographic Details
Published inAequationes mathematicae Vol. 94; no. 5; pp. 793 - 802
Main Authors Zeng, Xianhua, Huang, Xujian
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2020
Springer Nature B.V
Subjects
Analysis
Combinatorics
Mathematics
Mathematics and Statistics
Phase-isometry
type spaces
Primary 39B52
Secondary 46B04
Plus–minus linear isometry
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Summary:Let Γ , Δ be nonempty index sets, and let H ,  K be inner product spaces. We prove that for p ≥ 1 any surjective phase-isometry between ℓ p ( Γ , H ) and ℓ p ( Δ , K ) is a plus–minus linear isometry. This can be considered as an extension of Wigner’s theorem for real ℓ p ( Γ , H ) -type spaces.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-020-00723-4