On unbounded order continuous operators 2
Let E and F be two Archimedean Riesz spaces. An operator T : E → F is said to be unbounded order continuous ( uo -continuous), if u α → uo 0 in E implies T u α → uo 0 in F . In this study, our main aim is to give the solution to two open problems which are posed by Bahramnezhad and Azar. Using this,...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2024-02, Vol.28 (1), p.5, Article 5 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
E
and
F
be two Archimedean Riesz spaces. An operator
T
:
E
→
F
is said to be unbounded order continuous (
uo
-continuous), if
u
α
→
uo
0
in
E
implies
T
u
α
→
uo
0
in
F
. In this study, our main aim is to give the solution to two open problems which are posed by Bahramnezhad and Azar. Using this, we obtain that the space
L
uo
(
E
,
F
)
of order bounded unbounded order continuous operators is an ideal in
L
b
(
E
,
F
)
for Dedekind complete Riesz space
F
. In general, by giving an example that the space
L
uo
(
E
,
F
)
of order bounded unbounded order continuous operators is not a band in
L
b
(
E
,
F
)
, we obtain the conditions on
E
or
F
for the space
L
uo
(
E
,
F
)
to be a band in
L
b
(
E
,
F
)
. Then, we give the extension theorem for
uo
-continuous operators similar to Veksler’s theorem for order continuous operators. |
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| ISSN: | 1385-1292 1572-9281 |
| DOI: | 10.1007/s11117-023-01021-4 |