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Intersection of Two Invariant Subspaces

Published online by Cambridge University Press:  20 November 2018

Takahiko Nakazi
Takahiko Nakazi*
Affiliation:
Department of Mathematics Faculty of Science Hokkaido University Sapporo 060, Japan
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Abstract

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It is shown that, if F and G are inner functions, (H2 ⊖ FH2)/(H2 ⊖ FH2) ∩ GH2 is n-dimensional if and only if G is a Blaschke product of degree n. This is an extension of the well known result for the case (H2 ⊖ FH2) ∩ GH2 = {0}.

Keywords

Primary 47A1547B35Secondary 30D5530E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 129 - 133
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Ahern, P.R. and Clark, D.N., On functions orthogonal to invariant subspaces, Acta Math., 124 (1970), pp. 191–204.Google Scholar
2. Douglas, R.G., Banach Algebra Techniques in Operator Theory, Academic Press, New York.Google Scholar
3. Douglas, R.G., Shapiro, H.S. and Shields, A.L., Cyclic vectors and invariant subspaces for the backward shift operator, Ann. Inst. Fourier (Grenoble), 20 (1970), pp. 37–76.Google Scholar
4. Duren, P., Hp Spaces, Academic Press, New York, 1970.Google Scholar
5. Fisher, S.D., Algebras of bounded functions invariant under the restricted backward shift, J. Funct. Anal., 12 (1973), pp. 236–245.Google Scholar
6. Hayashi, E., Left invariant subspaces of H2 and the kernels of Toeplitz operators, in preprint.Google Scholar
7. Helson, H., Invariant Subspaces, Academic Press, New York, 1964.Google Scholar
8. Lee, M. and Sarason, D., The spectra of some Toeplitz operators, J. Math. Anal. Appl., 33 (1971), pp. 529–543.Google Scholar
9. Nakazi, T., The kernels of Toeplitz operators, J. Math. Soc. Japan, 38 (1986), 607–616.Google Scholar