Young's inequality in trace-class operators

 If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥₁ denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality. Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003 Mathematics Subject Classification (2000): 47A63, 15A60     

The C*-Envelope of an Irreducible Periodic Weighted Unilateral Shift

The C*-envelope of the 3-dimensional operator system generated by an irreducible periodic weighted unilateral shift operator is determined.     

The Weyl group and the normalizer of a conditional expectation

We define a discrete groupW(E) associated to a faithful normal conditional expectationE : M N forN M von Neuman algebras. This group shows the relation between the unitary groupU _N and the normalizerN _E ofE, which can be also considered as the isotropy of the action of the unitary groupU _M ofM onE. It is shown thatW(E) is finite if dimZ(N)< and bounded by the index in the factor case. Also sharp bounds of the order ofW(E) are founded.W(E) appears as the fibre of a covering space defined on the orbit ofE by the natural action of the unitary group ofM. W(E) is computed in some basic examples.     

On Tate's trace

The problem of whether Tate's trace is linear or not is reduced to a special case.     

On Tate's trace

The problem of whether Tate's trace is linear or not is reduced to a special case.     

A contractive version of a Schur-Horn theorem in II1 factors

We prove a contractive version of the Schur-Horn theorem for submajorization in II₁ factors that complements some previous results on the Schur-Horn theorem within this context. We obtain a reformulation of a conjecture of Arveson and Kadison regarding a strong version of the Schur-Horn theorem in II₁ factors in terms of submajorization and contractive orbits of positive operators.