A problem on products of Toeplitz operators
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- by Kun yu Guo PDF
- Proc. Amer. Math. Soc. 124 (1996), 869-871 Request permission
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
- Ronald G. Douglas, Banach algebra techniques in operator theory, Pure and Applied Mathematics, Vol. 49, Academic Press, New York-London, 1972. MR 0361893
Additional Information
- Received by editor(s): September 20, 1994
- Communicated by: Albert Baernstein II
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 869-871
- MSC (1991): Primary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-96-03224-8
- MathSciNet review: 1307521