Hokkaido Mathematical Journal

HASEGAWA Atsushi, JI Guoxing, OHWADA Tomoyoshi, SAITO Kichi-Suke,

Certain invariant subspace structure of $L^2(\Bbb T^2)$ II.

Hokkaido Mathematical Journal, 37 (2008) pp.493-505

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Abstract

Let M be an invariant subspace of L^2(T^2). Considering the largest z-invariant (resp. w-invariant) subspace F_z (resp. F_w) in the wandering subspace M \ominus zwM of M with respect to the shift operator zw. If F_w \ne {0} and F_z \ne {0}, then we consider the certain form of invariant subspaces M of L^2(T^2). Furthermore, we study certain classes of invariant subspaces of L^2(T^2).

MSC(Primary)47A15
MSC(Secondary)46L10
Uncontrolled Keywordsinvariant subspace, wandering subspace.