2023-04-02T02:37:32Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/689352022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Multipliers of invariant subspaces in the bidiscNakazi, T.open accessbidiscinvariant subspacemultipliers410For 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.Department of Mathematics, Hokkaido University1993-03engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83333http://hdl.handle.net/2115/6893510.14943/83333Hokkaido University Preprint Series in Mathematics189112https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/68935/1/pre189.pdfapplication/pdf291.98 KB1993-03