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WEIGHTED COMPOSITION OPERATORS WHOSE RANGES CONTAIN THE DISK ALGEBRA II
Izuchi, Kei Ji,Izuchi, Kou Hei,Izuchi, Yuko Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.
ZERO BASED INVARIANT SUBSPACES AND FRINGE OPERATORS OVER THE BIDISK
Izuchi, Kei Ji,Izuchi, Kou Hei,Izuchi, Yuko Korean Mathematical Society 2016 대한수학회지 Vol.53 No.4
Let M be an invariant subspace of $H^2$ over the bidisk. Associated with M, we have the fringe operator $F^M_z$ on $M{\ominus}{\omega}M$. It is studied the Fredholmness of $F^M_z$ for (generalized) zero based invariant subspaces M. Also ker $F^M_z$ and ker $(F^M_z)^*$ are described.
Weighted composition operators whose ranges contain the disk algebra II
Kei Ji Izuchi,Kou Hei Izuchi,Yuko Izuchi 대한수학회 2018 대한수학회보 Vol.55 No.2
Let $\{\p_n\}_{n\ge1}$ be a sequence of analytic self-maps of $\D$. It is proved that if the union set of the ranges of the composition operators $C_{\p_n}$ on the weighted Bergman spaces contains the disk algebra, then $\p_k$ is an automorphism of $\D$ for some $k\ge1$.
Zero based invariant subspaces and fringe operators over the bidisk
Kei Ji Izuchi,Kou Hei Izuchi,Yuko Izuchi 대한수학회 2016 대한수학회지 Vol.53 No.4
Let $M$ be an invariant subspace of $H^2$ over the bidisk. Associated with $M$, we have the fringe operator $F^M_z$ on $M\om w M$. It is studied the Fredholmness of $F^M_z$ for (generalized) zero based invariant subspaces $M$. Also ${\rm ker}\, F^M_z$ and ${\rm ker}\, (F^M_z)^*$ are described.
ESSENTIAL NORMS OF LINEAR COMBINATIONS OF COMPOSITION OPERATORS ON h<sup>∞</sup>
Izuchi, Kei Ji,Izuchi, Kou Hei Korean Mathematical Society 2013 대한수학회지 Vol.50 No.1
It is studied the linear combinations of composition operators on the Banach space of bounded harmonic functions on the open unit disk. We determine the essential norm of them.
CROSS COMMUTATORS ON BACKWARD SHIFT INVARIANT SUBSPACES OVER THE BIDISK II
Izuchi, Kei Ji,Izuchi, Kou Hei Korean Mathematical Society 2012 대한수학회지 Vol.49 No.1
In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [${S_z}^n$, $S_w^*$] = 0 for a positive integer n ${\geq}$ 2. In this case, it holds that ${S_z}^n=cI$ for some $c{\in}\mathbb{C}$. In this paper, it is proved that if [$S_{\varphi}$, $S_w^*$] = 0 and ${\varphi}{\in}H^{\infty}({\Gamma}_z)$, then $S_{\varphi}=cI$ for some $c{\in}\mathbb{C}$.
INTERPOLATIONS FOR HÖLDER'S INEQUALITY
Izuchi, Kei Ji,Izuchi, Kou Hei,Ohno, Shuichi Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
Kwon and Bae gave an interpolation for a continuous form of H$\ddot{o}$lder's inequality for a real-valued bounded measurable function on a product of measure spaces. It is given some generalizations of their result.
Essential norms of linear combinations of composition operators on h∞
Kei Ji Izuchi,Kou Hei Izuchi 대한수학회 2013 대한수학회지 Vol.50 No.1
It is studied the linear combinations of composition operators on the Banach space of bounded harmonic functions on the open unit disk. We determine the essential norm of them.
Cross commutators on backward shift invariant subspaces over the bidisk II
Kei Ji Izuchi,Kou Hei Izuchi 대한수학회 2012 대한수학회지 Vol.49 No.1
In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [Szn; S w] = 0 for a positive integer n 2. In this case, it holds that Szn = cI for some c 2 C. In this paper, it is proved that if [Sφ; S w] = 0and φ 2 H1(z), then Sφ = cI for some c 2 C.
Interpolations for Holder's inequality
Kou Hei Izuchi,Ken Ji Izuchi,Shuichi Ohno 대한수학회 2013 대한수학회보 Vol.50 No.3
Kwon and Bae gave an interpolation for a continuous form of Holder's inequality for a real-valued bounded measurable function on a product of measure spaces. It is given some generalizations of their result.