Remarks on Isometries of Products of Linear Spaces - Archive ouverte HAL Access content directly
Journal Articles Extracta Mathematicae Year : 2015

## Remarks on Isometries of Products of Linear Spaces

(1)
1
Mohammed Bachir
• Function : Author
• PersonId : 960537

#### Abstract

Given two normed spaces $X$ , $Y$ , the aim of this paper is establish that the existence of an isomorphism isometric between $X \times R$ and $Y \times R$ is equivalent to the existence of an isometric isomorphism between $X$ and $Y$ , provided the norms satisfy an appropriate condition. By means of a counterexample, it is shown that this result fails for arbitrary norms even if $X = Y = R^2$.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-01183199 , version 1 (06-08-2015)

### Identifiers

• HAL Id : hal-01183199 , version 1

### Cite

Mohammed Bachir. Remarks on Isometries of Products of Linear Spaces. Extracta Mathematicae, 2015, 30 (1), pp.1-13. ⟨hal-01183199⟩

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