If T= U ∣ T ∣ denotes the polar decomposition of a bounded linear operator T, then the
Aluthge transform of T is defined to be the operator ̃ T= ∣ T ∣^ 1 2 U ∣ T ∣^ 1 2. In this …

In this paper, we reprove that:(i) the Aluthge transform of a complex symmetric operator ̃ T=|
T|^ 1 2 U| T|^ 1 2 is complex symmetric,(ii) if T is a complex symmetric operator, then (̃ T) …

Let H be a complex infinite-dimensional Hilbert space, let B (H) denote the algebra of
bounded linear operators on H, and let T∈ B (H). For T≡ V| T| the canonical polar …

Let H and K be two Hilbert spaces. The algebra of all bounded linear operators acting on H
is denoted by B (H). The main purpose of this paper is to obtain a characterization of …

Given an r× r complex matrix T, if T= U| T| is the polar decomposition of T, then, the Aluthge
transform is defined by Let Δn (T) denote the n-times iterated Aluthge transform of T, ie, Δ0 …

In this paper, we explore various transforms associated with a bounded linear operator T on
a Hilbert space. These transforms include the Aluthge, λ-Aluthge, Duggal, generalized …

Let $ T\in\mathcal {B}(\mathcal {H}) $ be a bounded linear operator on a Hilbert space
$\mathcal {H} $, and let $ T\equiv V| T| $ be the polar decomposition of $ T $. The mean …

Abstract Let A= U| A| and B= V| B| be the polar decompositions of A ∈ B (H _1) and B ∈ B
(H _2) and let Com (A, B) stand for the set of operators X ∈ B (H _2, H _1) such that AX= XB …

Let B (H) be the algebra of all bounded linear operators acting on a Hilbert space H. The
main purpose in this paper is to obtain a characterization of bijective maps Φ: B (H)→ B (K) …

We introduce the concept of ϵ-homoclinic points for invertible linear operators on Banach
spaces. We establish that an operator is hyperbolic if and only if it possesses the shadowing …