Fuglede theorem for symmetric spaces of $τ$-measurable operators
Authors
Denis Potapov
Fedor Sukochev
Anna Tomskova
Dmitriy Zanin
Abstract
We extend the classical Fuglede commutativity theorem to the full scale of symmetrically normed operator ideals. Our main result provides a complete characterization: a symmetric ideal or symmetric operator space of $τ$-measurable operators satisfies the Fuglede theorem if and only if its commutative core has non-trivial Boyd indices, or equivalently, if it is an interpolation space in the scale of $L_p$-spaces for $1
