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Multipliers of invariant subspaces in the bidisc
| Title: | Multipliers of invariant subspaces in the bidisc |
| Authors: | Nakazi, T. Browse this author |
| Keywords: | bidisc | | invariant subspace | | multipliers |
| Issue Date: | Mar-1993 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 189 |
| Start Page: | 1 |
| End Page: | 12 |
| Abstract: | For any nonzero invariant subspace M in H2 (T2), set M x = [ U z nM] n [ U w nM] then Mx is also an invariant subspace of H2 (T2) that contains M .. If M is of finite codimension in H2 (T2 ) then M>< = H2 (T2 ) and if M = qH2 (T2 ) for some inner function q then M>< = M. In this paper invariant subspaces with M:>< =Mare studied. If M = q1H2 (T2 )nq2 H2 (T2 ) and q1, q2 are inner functions then Mx = M. However in general this invariant subspace may not be of the form : qH2 (T2 ) for some inner function q. Put /ll(M) = {¢<: L00 :¢M H2 (T2 )} then hz(M) is described and rJZ(M) = )n.(M'J< ) is shown. This is the set of all multipliers of Min the title. A necessary and sufficient condition for /11(M) = t0(T2 ) is given. It is noted that the kernel of a Hankel operator is an invariant subspace M with Mx = M. The argument applies to the polydisc case. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/68935 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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