On the spectrum of the upper triangular double band matrix U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
Abstract
The upper triangular double band matrix
U
(
a
0
,
a
1
,
a
2
;
b
0
,
b
1
,
b
2
)
is defined on a Banach sequence space by
U
(
a
0
,
a
1
,
a
2
;
b
0
,
b
1
,
b
2
)
(
x
n
)
=
(
a
n
x
n
+
b
n
x
n
+
1
)
∞
n
=
0
where
a
x
=
a
y
,
b
x
=
b
y
for
x
≡
y
(
m
o
d
3
)
. The class of the operator
U
(
a
0
,
a
1
,
a
2
;
b
0
,
b
1
,
b
2
)
includes, in particular, the operator
U
(
r
,
s
)
when
a
k
=
r
and
b
k
=
s
for all
k
∈
N
, with
r
,
s
∈
R
and
s
≠
0
. Also, it includes the upper difference operator;
a
k
=
1
and
b
k
=
−
1
for all
k
∈
N
. In this paper, we completely determine the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator
U
(
a
0
,
a
1
,
a
2
;
b
0
,
b
1
,
b
2
)
over the sequence space
c
.
Description
Keywords
Upper triangular band matrix, spectrum, fine spectrum, approximate point spectrum