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Department of Mathematics, University of Kuwait

ABSTRACT

Let S be the unit sphere in the n-dimensional complex space Cⁿ. In this paper it is shown that the Toeplitz operator T_ø* defined on the Hardy space H²(S) with symbol ø^*an element in H ^∞( S ) such that (ø^*)^-1 exists in L ^∞ (S) is Fredholm. Moreover (ø^*)^-1 is in H ^∞ (S).