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SPLITTING INVARIANT SUBSPACES IN THE HARDY SPACE OVER THE BIDISK

Published online by Cambridge University Press:  12 May 2016

KEI JI IZUCHI*
Affiliation:
Department of Mathematics, Niigata University, Niigata 950-2181, Japan email izuchi@m.sc.niigata-u.ac.jp
KOU HEI IZUCHI
Affiliation:
Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753-8511, Japan email izuchi@yamaguchi-u.ac.jp
YUKO IZUCHI
Affiliation:
Aoyama-shinmachi 18-6-301, Nishi-ku, Niigata 950-2006, Japan email yfd10198@nifty.com
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Abstract

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Let $H^{2}$ be the Hardy space over the bidisk. It is known that Hilbert–Schmidt invariant subspaces of $H^{2}$ have nice properties. An invariant subspace which is unitarily equivalent to some invariant subspace whose continuous spectrum does not coincide with $\overline{\mathbb{D}}$ is Hilbert–Schmidt. We shall introduce the concept of splittingness for invariant subspaces and prove that they are Hilbert–Schmidt.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author is partially supported by Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science (no. 24540164).

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