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# Multipliers of invariant subspaces in the bidisc

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 Title: Multipliers of invariant subspaces in the bidisc Authors: Nakazi, T. Browse this author Keywords: bidisc invariant subspace multipliers Issue Date: Mar-1993 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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