On Representations of Fredholm and Semi-Fredholm Spectra of Multi-Toeplitz Operators with Symbols in H`qC

In this paper, we give the representations of Fredholm and semi-Fredholm spectra of multi-Toeplitz operators with symbols in H` qC, and prove that, for w1, . . . , wngH`qC nG2., if Tw1, . . . ,Twn.is Fredholm, then ind Tw1, . . . ,Twn. s0, in contrast with the case of one operator.