Reducing Subspaces for Toeplitz Operator Tz1k1z2k2+az¯1l1z¯2l2 on the Weighted Hardy Space over the Bidisk. (26th March 2022) - Wei, Changguo; Ding, Xin; Shi, Yanyue
Abstract : In this paper, we completely characterize the reducing subspaces for T φ a on weighted Hardy space ℋ ω 2 D 2 under three assumptions on ω, where φ a = z k + a z ¯ l, k, l ∈ ℕ 2, k ≠ l, and a ∈ 0, 1 . It is shown that the coefficient a ∈ 0, 1 does not affect the reducing subspaces for T φ a . We also prove that, for every δ > 0, weighted Dirichlet space D δ 2 D 2 is a weighted Hardy space which satisfies these assumptions. As an application, we describe the reducing subspaces for T φ a on D δ 2 D 2 and get the structure of commutant algebra V ∗ T φ a .