Measurable bundles of \(C^*\)-algebras. (Russian) Zbl 1051.46053

Ganiev, I. G.; Chilin, V. I.

Vladikavkaz. Mat. Zh. 5, No. 1, 35-38 (2003).

It is proved that an involutive Banach-Kantorovich algebra over the ring of all measurable functions whose norm satisfies some conditions that are analogous to the axioms of a \(C^*\)-algebra admits a unique up to \(*\)-isometry representation by a measurable bundle of \(C^*\)-algebras with vector-valued lifting.

Reviewer: S. A. Malyugin (Novosibirsk)

MSC:

46L89	Other “noncommutative” mathematics based on \(C^*\)-algebra theory
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

Banach bundle; Banach algebra