Some $\mathbb{A}$-numerical radius inequalities for $d\times d$ operator matrices

Abstract

Let A be a positive (semidefinite) bounded linear operator acting on a complex Hilbert space H, • | • . The semi-inner product x | y A := Ax | y , x, y ∈ H induces a seminorm • A on H. Let T be an A-bounded operator on H, the A-numerical radius of T is given byIn this paper, we establish several inequalities for ω A (T), where T = (T ij ) is a d × d operator matrix with T ij are A-bounded operators and A is the diagonal operator matrix whose each diagonal entry is A.

Further inequalities for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices

“…Recently, several inequalities for the A-numerical radius of 2×2 operator matrices have been established by P. Bhunia et al and Rout et al when A is a positive injective operators (see [8,19]). Moreover, different upper and lower bounds of A-numerical radius when A is a positive semidefinite operator has been recently investigated by the first author in [13]. In this article, we will continue working in this direction and we will prove several new A-numerical radius inequalities of certain 2 × 2 operator matrices.…”

Further results on $\mathbb{A}$-numerical radius inequalities

“…In this year, Bhunia et al [4,5] presented several A-numerical radius inequalities for a strictly positive operator A. Feki [8], and Feki and Sahoo [9] established some more A-numerical radius inequalities under the assumption "N (A) ⊥ is invariant under different operators". We refer the interested reader to [10,17] and the references cited therein for further generalizations and refinements of A-numerical radius inequalities. The objective of this paper is to present a few new A-numerical radius inequalities for 2×2 and n × n operator matrices.…”

On $\mathbb{A}$-numerical radius inequalities for $2\times2$ operator matrices-II

“…In 2020, Bhunia et al [8] obtained several A-numerical radius inequalities. For more results on A-numerical radius inequalities we refer the reader to visit [10,18,23,12]. In 2020, the concept of the A-spectral radius of A-bounded operators was introduced by Feki in [11] as follows:…”