Bohr compactifications of topological algebraic structures and almost periodic functions
by
Salvador Hernandez
Universitat Jaume I

The Bohr compactification is a well known construction for (topological) groups and semigroups. Recently, this notion has been generalized and investigated for arbitrary algebraic structures. In this case, the Bohr compactification is defined as the maximal compactification which is compatible with the structure involved. Here, given any (topological) algebraic structure, the definition of almost periodic function f is introduced in terms of translates of f and with no reference to any compactification of the underlying structure. Thus, the Bohr compactification of any (topological) algebraic structure is characterized as the Gelfand space associated to the commutative Banach algebra of all almost periodic functions what has been the initial definition for groups and semigroups. An application is given to the representation of isometries defined between spaces of almost periodic functions.

Date received: May 15, 2003