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Projective freeness and stable rank of algebras of complex-valued BV functions
Published online by Cambridge University Press: 16 January 2023
The paper investigates the algebraic properties of weakly inverse-closed complex Banach function algebras generated by functions of bounded variation on a finite interval. It is proved that such algebras have Bass stable rank 1 and are projective-free if they do not contain nontrivial idempotents. These properties are derived from a new result on the vanishing of the second Čech cohomology group of the polynomially convex hull of a continuum of a finite linear measure described by the classical H. Alexander theorem.
- Canadian Mathematical Bulletin , First View , pp. 1 - 10
- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Research is supported in part by NSERC.