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Spectral radius of semi-Hilbertian space operators and its applications
In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space H , which are bounded with respect to the seminorm induced by a positive operator A on H . Mainly, we show that r A ( T ) ≤ ω A ( T ) for every A -bounded operator T , w...
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| Published in: | Annals of functional analysis 2020-09, Vol.11 (4), p.929-946 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space
H
, which are bounded with respect to the seminorm induced by a positive operator
A
on
H
. Mainly, we show that
r
A
(
T
)
≤
ω
A
(
T
)
for every
A
-bounded operator
T
, where
r
A
(
T
)
and
ω
A
(
T
)
denote respectively the
A
-spectral radius and the
A
-numerical radius of
T
. This allows to establish that
r
A
(
T
)
=
ω
A
(
T
)
=
‖
T
‖
A
for every
A
-normaloid operator
T
, where
‖
T
‖
A
is denoted to be the
A
-operator seminorm of
T
. Moreover, some characterizations of
A
-normaloid and
A
-spectraloid operators are given. |
|---|---|
| ISSN: | 2639-7390 2008-8752 |
| DOI: | 10.1007/s43034-020-00064-y |