On Algebras of Continuous Functions
نویسنده
چکیده
Let C denote the algebra of functions continuous on the unit circle. With norm ||/¡| =sup¡xi-i \f(X)\, C is a Banach algebra. Let A denote the set of all / in C which are boundary values of functions analytic in \z\ <1 and continuous in \z\ ál. A is then a closed subalgebra of C, and by known results A consists of those and only those/ in C for which /|X|-l/(X)XBdX = 0, «^0. In [l ] the question was raised whether if and A is all of C. It was shown in [l ] that if (¡> is real or if satisfies a Lipschitz condition, then the algebra generated by A and <b does equal C. In the following theorem the question is answered in the affirmative.
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