On the 𝐶*-algebra of Toeplitz operators on the quarterplane

Douglas, R. G.; Howe, Roger

doi:10.1090/S0002-9947-1971-0288591-1

On the $C^*$-algebra of Toeplitz operators on the quarterplane
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by R. G. Douglas and Roger Howe PDF

Trans. Amer. Math. Soc. 158 (1971), 203-217 Request permission

Abstract:

Using the device of the tensor product of ${C^ \ast }$-algebras, we study the ${C^ \ast }$-algebra generated by the Toeplitz operators on the quarter-plane. We obtain necessary and sufficient conditions for such an operator to be Fredholm, but show in this case that not all such operators are invertible.

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