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A problem on products of Toeplitz operators

Author: Kun yu Guo
Journal: Proc. Amer. Math. Soc. 124 (1996), 869-871
MSC (1991): Primary 47B35
MathSciNet review: 1307521
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Abstract: A natural and interesting problem on classical Hardy space of one complex variable is the following:

Problem: If $T_{\varphi_1}T_{\varphi_2}\dotsb T_{\varphi_n}=0$, then there exist some $i$ such that $\varphi_i=0$.

In this note, we establish the kernel inclusion theorem for the products of Toeplitz operators. Using this fact, in case $n=5$, we give the above question an affirmative answer.

References [Enhancements On Off] (What's this?)

  • 1. 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