n-Tuples of operators satisfying σT(AB)=σT(BA)

AbstractFor “criss-cross commuting” tuples A and B of Banach space operators we give two sufficient conditions for the spectral equality σT(AB)=σT(BA)

A remark on the slice map problem

It is shown that there exist a σ-weakly closed operator algebra A˜, generated by finite rank operators and a σ-weakly closed operator algebra B˜ generated by compact operators such that the Fubini product A˜⊗¯FB˜ contains properly A˜⊗¯B˜

Singular integral models for p-hyponormal operators and the Riemann-Hilbert problem

The purpose of this paper is to give singular integral models for p-hyponormal operators and apply them to the Riemann-Hilbert problem

Separable injectivity and C*-tensor products

Let A and B be C*-algebras and let D be a C*-subalgebra of B. We show that if D is separably injective then the triple (A,B,D) verifies the slice map conjecture. As an application, we prove that the minimal C*-tensor product A⊗B is separably injective if and only if both A and B are separably injective and either A or B is finite-dimensional