Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H.  Let N be a unitary invariant norm  defined on a norm ideal I ⊆ L(H)$. Given two positive invertible operators P, Q ∈ L(H) and k ∈ (-2,2], ...

For each n × n positive semidefinite matrix A we define the minimal index I (A)=max{λ ⪰ 0 : A ο B ⪰ λB for all B ⪰ 0} and, for each norm N, the N-index I_N(A) = min{N(A ο B): B ⪰0 and N(B) = 1}, where A ο B = [aij bij] is ...

In this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm. Among the well-known inequalities which can be proved with this technique are the Löwner–Heinz ...

We describe properties of a Hermitian matrix M ∈ Mn(C) having minimal quotient norm in the following sense: M M + D for all real diagonal matrices D ∈ Mn(C). Here denotes the operator norm. We show a constructive method ...

A conjecture posed by S. Hayajneh and F. Kittaneh claims that given A, B positive matrices, 0≤t≤1, and any unitarily invariant norm the following inequality holds{triple vertical-rule fence}AtB1-t+BtA1-t{triple vertical-rule ...