A problem on products of Toeplitz operators
Abstract: A natural and interesting problem on classical Hardy space of one complex variable is the following:
Problem: If , then there exist some such that .
In this note, we establish the kernel inclusion theorem for the products of Toeplitz operators. Using this fact, in case , we give the above question an affirmative answer.
- R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972 MR 50:14335
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Received by editor(s): September 20, 1994
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society