DOI: 10.68381/jca31013 ISSN: 0944-6532
A-Numerical Radius of Semi-Hilbert Space Operators
Messaoud Guesba, Pintu Bhunia, Kallol Paul
Let
\mathbf{A=}\left(\!\! \begin{array}{cc} A & 0 \\ 0 & A \end{array}\!\! \right)
A
=
(
A
0
0
A
)
be a
2\times 2
2
×
2
diagonal operator matrix whose each diagonal entry is a positive bounded linear operator
A
A
acting on a complex Hilbert space
{\mathcal{H}}
H
. Let
T,S
T
,
S
and
R
R
be bounded linear operators on
{\mathcal{H}}
H
admitting
A
A
-adjoints, where
T
T
and
R
R
are
A
A
-positive. By considering an
\mathbf{A}
A
-positive
2 \times 2
2
×
2
operator matrix
\left(\!\!\begin{array}{cc}T & S^{^{\sharp _{A}}} \\S & R \end{array}\!\!\right)
(
T
S
♯
A
S
R
)
, we develop several upper bounds for the
A
A
-numerical radius of
S
S
. Applying these upper bounds we obtain new
A
A
-numerical radius bounds for the product and the sum of arbitrary operators which admit
A
A
-adjoints. Related other inequalities are also derived.