Toeplitz operators with symbols from in the spaces

It is shown that the algebra of the multipliers of the space ^p (1<<) contains the closed subalgebra C_p+H_p, which coincides with the Douglas algebra C + H for =2. It is proved that a Toeplitz operator with symbol from C_p+H_p is Fredholm on ^p if and only if its symbol is invertible in C_p+H_p.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 124–128, 1987.The authors are grateful to V. I. Vasyunin for assistance.