The spectrum of an element in a Banach-Kantorovich algebra over a ring of measurable functions

摘要

It is established that every Banach-Kantorovich algebra over a ring of measurable functions can be represented as a measurable bundle of Banach algebras with a vector-valued lifting. Using this representation we prove non emptiness and cyclic compactness of the spectrum of an element in a Banach-Kantorovich algebra over a ring of measurable functions. Further we give some applications of the main result to bounded homomorphisms on Kaplansky-Hilbert modules and partial integral operators on function spaces with a mixed norm.