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We denote by A_0+AP_+ the Banach algebra of all complex-valued functions fdefined in the closed right half plane, such that f is the sum of a holomorphicfunction vanishing at infinity and a ``causal'' almost periodic function. Wegive a complete description of the maximum ideal space M(A_0+AP_+) of A_0+AP_+.Using this description, we also establish the following results:  (1) The corona theorem for A_0+AP_+.  (2) M(A_0+AP_+) is contractible (which implies that A_0+AP_+ is a projectivefree ring).  (3) A_0+AP_+ is not a GCD domain.  (4) A_0+AP_+ is not a pre-Bezout domain.  (5) A_0+AP_+ is not a coherent ring.  The study of the above algebraic-anlaytic properties is motivated byapplications in the frequency domain approach to linear control theory, wherethey play an important role in the stabilization problem.

A subalgebra of the Hardy algebra relevant in control theory and its algebraic-analytic properties