Maps Preserving the Norm of the Positive Sum in Lp Spaces
For 1 < p < ∞, let S ( L p ) + be the set of positive elements in L p with norm one. Assume that V 0 : S ( L p (Ω 1 )) + → S ( L p (Ω 2 )) + is a surjective norm-additive map; that is, In this paper, we show that V 0 can be extended to an isometry from L p (Ω 1 ) onto L p (Ω 2 ).
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| Veröffentlicht in: | Acta mathematica scientia 2022-03, Vol.42 (2), p.789-794 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | For 1 <
p
< ∞, let
S
(
L
p
)
+
be the set of positive elements in
L
p
with norm one. Assume that
V
0
:
S
(
L
p
(Ω
1
))
+
→
S
(
L
p
(Ω
2
))
+
is a surjective norm-additive map; that is,
In this paper, we show that
V
0
can be extended to an isometry from
L
p
(Ω
1
) onto
L
p
(Ω
2
). |
|---|---|
| ISSN: | 0252-9602 1572-9087 |
| DOI: | 10.1007/s10473-022-0223-8 |