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SynopsisIn this paper the Sturm-Liouville regular boundary value problem and expansion theorem is extended to functions with values in some B*-algebras.

ABSTRACT. The main result in this paper states that the second order linear B*-algebra differential equation {p(t)y') + q{t)y = 0, where p{t) is positive and q(t) is Hermitian for each t, is nonoscillatory on [io,co) if the scalar equation (IIP^Mir1^")' + ll