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.

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= { ...

We study the geometry of the set p, with 1 < p < ∞, which consists of perturbations of the identity operator by p-Schatten class operators, which are positive and invertible as elements of B(H). These manifolds have 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 ...

The aim of this work is to apply the complex interpolation method to norms of n-tuples of operators in the p-Schatten classes of a Hilbert space H. The norms considered define Finsler metrics in a certain manifold of ...

We study three well-known minimization problems in Hilbert spaces: the weighted least squares problem and the related problems of abstract splines and smoothing. In each case we analyze the solvability of the problem for ...

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 ...

Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator such that W^1/2 is in the p-Schatten class, for some 1 ≤ p < ∞. Given A,B ∈ L(H) with closed range and C ∈ L(H), ...

The largest volume ratio of a given convex body K ⊂ Rn is defined as lvr(K) := sup L⊂Rn vr(K, L), where the sup runs over all the convex bodies L. We prove the following sharp lower bound: c √n ≤ lvr(K), for every body K ...