Bilinear isometries on spaces of vector-valued continuous functions
Let X, Y, Z be compact Hausdorff spaces and let E 1 , E 2 , E 3 be Banach spaces. If T : C ( X , E 1 ) × C ( Y , E 2 ) → C ( Z , E 3 ) is a bilinear isometry which is stable on constants and E 3 is strictly convex, then there exist a nonempty subset Z 0 of Z, a surjective continuous mapping h : Z 0...
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| Vydáno v: | Journal of mathematical analysis and applications Ročník 385; číslo 1; s. 340 - 344 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
2012
|
| Témata: | |
| ISSN: | 0022-247X, 1096-0813 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Let
X,
Y,
Z be compact Hausdorff spaces and let
E
1
,
E
2
,
E
3
be Banach spaces. If
T
:
C
(
X
,
E
1
)
×
C
(
Y
,
E
2
)
→
C
(
Z
,
E
3
)
is a bilinear isometry which is stable on constants and
E
3
is strictly convex, then there exist a nonempty subset
Z
0
of
Z, a surjective continuous mapping
h
:
Z
0
→
X
×
Y
and a continuous function
ω
:
Z
0
→
B
i
l
(
E
1
×
E
2
,
E
3
)
such that
T
(
f
,
g
)
(
z
)
=
ω
(
z
)
(
f
(
π
X
(
h
(
z
)
)
)
,
g
(
π
Y
(
h
(
z
)
)
)
)
for all
z
∈
Z
0
and every pair
(
f
,
g
)
∈
C
(
X
,
E
1
)
×
C
(
Y
,
E
2
)
. This result generalizes the main theorems in Cambern (1978)
[2] and Moreno and Rodríguez (2005)
[7]. |
|---|---|
| ISSN: | 0022-247X 1096-0813 |
| DOI: | 10.1016/j.jmaa.2011.06.054 |