Email: i.doust@unsw.edu.au
Abstract: Motivated by problems in the spectral theory of linear operators the authors previously introduced a new concept of variation for functions defined on a nonempty compact subset of the plane. In this paper we examine the algebras of functions of bounded variation one obtains from these new definitions for the case where the underlying compact set is either a rectangle or the unit circle, and compare these algebras with the ones previously used by Berkson and Gillespie in their theories of $AC$-operators and trigonometrically well-bounded operators.
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