Operator Algebra Generated by an Element from the Module B(V1,V2)
Let B ∈ B ( V 1 ) , A ∈ B ( V 2 ) and X ∈ B ( V 1 , V 2 ) be given operators. In this paper the algebra A AXB generated by AXB is defined. Some results are obtained regarding invertibility in A AXB . Special cases and extensions are discussed using algebraic representations. Applications to the oper...
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| Veröffentlicht in: | Complex analysis and operator theory 2019-07, Vol.13 (5), p.2381-2409 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
B
∈
B
(
V
1
)
,
A
∈
B
(
V
2
)
and
X
∈
B
(
V
1
,
V
2
)
be given operators. In this paper the algebra
A
AXB
generated by
AXB
is defined. Some results are obtained regarding invertibility in
A
AXB
. Special cases and extensions are discussed using algebraic representations. Applications to the operator equations
A
X
=
C
,
X
B
=
C
,
A
X
B
=
C
,
X
-
A
X
B
=
C
and
A
X
-
X
B
=
C
are illustrated. |
|---|---|
| ISSN: | 1661-8254 1661-8262 |
| DOI: | 10.1007/s11785-019-00899-x |