We study jointly quasinormal and spherically quasinormal pairs of commuting operators on
Hilbert space, as well as their powers. We first prove that, up to a constant multiple, the only …

In this paper, we introduce the notion of generalized spherical Aluthge transforms for
commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) …

Let re (S) be the Euclidean spectral radius associated with aq-tuple S=(S 1,…, S q) of
bounded linear operators on a complex Hilbert space. The principal objective of our study is …

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 $\mathbf {T}=(T_1,\ldots, T_d) $ be a $ d $-tuple of operators on a complex Hilbert space
$\mathcal {H} $. The spherical Aluthge transform of $\mathbf {T} $ is the $ d $-tuple given by …

We first discuss the spherical Aluthge and spherical Duggal transforms for commuting pairs
of operators on Hilbert space. Second, we study the fixed points of these transforms, which …

In the first part of this paper, we introduce two notions of multivariable Duggal transforms
(toral and spherical), and study their basic properties including hyponormality and norm …

In this paper,(f, g)-spherical Aluthge transform for the tuples of operators is introduced, as an
extension of the classical Aluthge transform, and its continuity in the norm topology is given …

For an arbitrary commuting d–tuple T of Hilbert space operators, we fully determine the
spectral picture of the generalized spherical Aluthge transform Δ t (T) and we prove that the …

Abstract Let T=(T 1,…, T d) be ad-tuple of bounded linear operators on a complex Hilbert
space H. Recently, Benhida et al. defined the generalized spherical Aluthge transform of T …