In this paper, we obtain some refinements of the known operator inequalities for the p-Schatten class. In addition, we obtain an approach to the inequalities conjectured by Audenaert and Kittaneh for the p-Schatten class.

If X is the set of compact or p-Schatten operators over a complex Hilbert separable space H, we study the existence and characterization properties of Hermitian A∈X such that |||A|||≤|||A+D|||,for allD∈D(X) or equivalently ...

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in-Schatten ideals. In addition, we investigate the problem of characterization of norm-parallelism for bounded linear ...

Let T∈ L(H), and let T=U|T|= |T*| U be the polar decomposition of T . Then, for every λ∈[0,1], the λ-Aluthge transform is defined by D λ (T )= |T| l U|T| 1-λ . We show that several properties which are known for the usual ...

Let H= H+⊕ H- be a fixed orthogonal decomposition of the complex separable Hilbert space H in two infinite-dimensional subspaces. We study the geometry of the set Pp of selfadjoint projections in the Banach algebra Ap= { ...

Let S(H) be the unit sphere of a Hilbert space H and Up(H) thegroup of unitary operators in H such that u−1 belongs to the p-Schatten idealBp(H). This group acts smoothly and transitively in S(H) and endows it witha natural ...

We apply the complex interpolation method to prove that, given two spaces B (n) p0,a;s0 , B(n) p1,b;s1 of n-tuples of operators in the p-Schatten class of a Hilbert space H, endowed with weighted norms associated to positive ...

We consider norms on a complex separable Hilbert space such that ⟨aξ,ξ⟩≤‖ξ‖2≤⟨bξ,ξ⟩ for positive invertible operators a and b that differ by an operator in the Schatten class. We prove that these norms have unitarizable ...