open access

https://doi.org/10.14943/83333

https://hdl.handle.net/2115/68935

Multipliers of invariant subspaces in the bidisc

英語

multipliers

1993-03

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

189

1-12

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.

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