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n-SOT Hypercyclic Linear Maps on Banach Algebra of Operators
Let B ( X ) be the algebra of bounded linear operators on a Banach space X . A subset E of B ( X ) is said to be n -SOT dense in B ( X ) if for every continuous linear operator Λ from B ( X ) onto X ( n ) , the direct sum of n copies of X , Λ ( E ) is dense in X ( n ) . We consider the n -SOT hyperc...
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| Published in: | Bulletin of the Iranian Mathematical Society 2019-04, Vol.45 (2), p.411-427 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
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| Summary: | Let
B
(
X
) be the algebra of bounded linear operators on a Banach space
X
. A subset
E
of
B
(
X
) is said to be
n
-SOT dense in
B
(
X
) if for every continuous linear operator
Λ
from
B
(
X
) onto
X
(
n
)
, the direct sum of
n
copies of
X
,
Λ
(
E
)
is dense in
X
(
n
)
. We consider the
n
-SOT hypercyclic continuous linear maps on
B
(
X
), namely, those that have orbits that are
n
-SOT dense in
B
(
X
). Some nontrivial examples of such operators are provided and many of their basic properties are investigated. In particular, we show that the left multiplication operator
L
T
is 1-SOT hypercyclic if and only if
T
is hypercyclic on
X
. |
|---|---|
| ISSN: | 1017-060X 1735-8515 |
| DOI: | 10.1007/s41980-018-0140-8 |