DOI: 10.68381/jca29010 ISSN: 0944-6532
Some Remarks on Orthogonality of Bounded Linear Operators
Anubhab Ray, Kallol Paul, Debmalya Sain, Subhrajit Dey
We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if
T, A \in \mathbb{L}(\mathbb{X}, \mathbb{Y})
T
,
A
∈
L
(
X
,
Y
)
satisfy
T \bot_B A
T
⊥
B
A
, then whether there exists
x \in \mathbb{X}
x
∈
X
such that
Tx\bot_B Ax
T
x
⊥
B
A
x
with
\|x\| =1
∥
x
∥
=
1
,
\|Tx\| = \|T\|
∥
T
x
∥
=
∥
T
∥
, where
\mathbb{X}, \mathbb{Y}
X
,
Y
are normed linear spaces. In this context, we introduce the notion of Property
P_n
P
n
for a Banach space and illustrate its connection with orthogonality of a bounded linear operator between Banach spaces. We further study Property
P_n
P
n
for various polyhedral Banach spaces.