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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03224-8
PII: S 0002-9939(96)03224-8
Received by editor(s): September 20, 1994
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society