Let H be a Hilbert space and let A be a positive bounded operator on H. An operator T∈ B
(H) is said to be A-invertible if there exists S∈ B (H) such that ATS= AST= A. In this paper we …

Let H be a complex Hilbert space, and A be a positive bounded linear operator on H. Let BA
(H) denote the set of all bounded linear operators on H whose A-adjoint exists. Let A denote …

Let A be a positive (semidefinite) bounded linear operator acting on a complex Hilbert
space\big (H, ⟨ ⋅, ⋅ ⟩\big)(H,⟨·,·⟩). The semi-inner product ⟨ x, y ⟩ _A:= ⟨ Ax, y ⟩⟨ x, y⟩ …

This paper deals mainly with some aspects of the adjointable operators on Hilbert C∗-
modules. A new tool called the generalized polar decomposition for each adjointable …

Let P and Q be projections on a Hilbert C⁎-module. Under the orthogonal decomposition
raised by the range and the null space of P, some new results on the 2× 2 matrix …

We introduce the notion of a tractable pair of operators as well as that of the generalized
parallel sum in the setting of adjointable operators on Hilbert C∗-modules. Some significant …

Let E be a Hilbert C⁎-module and L (E) be the C⁎-algebra of adjointable operators on E.
We extend a work of Pedersen and Takesaki to the setting of Hilbert C⁎-modules by giving …

The main goal of this article is to establish several new A A-numerical radius equalities for n
* nn× n circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal …

The main goal of this article is to establish several new A-numerical radius equalities and
inequalities for n× n cross-diagonal, left circulant, skew left circulant operator matrices …

The main purpose of this paper is, in the general setting of the adjointable operators on
Hilbert C∗-modules, to develop two new tools that can be applied to deal with the positive …