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Hypercyclic operator weighted shifts
Munmun Hazarika,S. C. Arora 대한수학회 2004 대한수학회보 Vol.41 No.4
We consider bilateral operator weighted shift T onmathbf{L}^2(mathcal{K}) with weight sequence{A_n}_{n=-infty}^infty of positive invertible diagonaloperators on mathcal{K}. We give a characterization for T tobe hypercyclic, and show that the conditions are far simplified incase T is invertible.
HYPERCYCLIC OPERATOR WEIGHTED SHIFTS
Hazarika, Munmun,Arora, S.C. Korean Mathematical Society 2004 대한수학회보 Vol.41 No.4
We consider bilateral operator weighted shift T on $L^2$(K) with weight sequence ${[A_{n}]_{n=-{\infty}}}^{\infty}$ of positive invertible diagonal operators on K. We give a characterization for T to be hypercyclic, and show that the conditions are far simplified in case T is invertible.
On hyponormality of Toeplitz operators with polynomial and symmetric type symbols
Munmun Hazarika,Ambeswar Phukon 대한수학회 2011 대한수학회보 Vol.48 No.3
In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur's algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur's functions [기호]_0, [기호]_1 and [기호]_2. Here we explicitly evaluate the Schur's function [기호]_3. Using this value we find necessary and sufficient conditions under which the Toeplitz operator T_φ is hyponormal, where φ is a trigonometric polynomial given by φ (z)=[수식] and satisfies the condition [수식]. Finally we illustrate the easy applicability of the derived results with a few examples.
ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS
Hazarika, Munmun,Phukon, Ambeswar Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3
In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur's algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur's functions ${\Phi}_0$, ${\Phi}_1$ and ${\Phi}_2$. Here we explicitly evaluate the Schur's function ${\Phi}_3$. Using this value we find necessary and sufficient conditions under which the Toeplitz operator $T_{\varphi}$ is hyponormal, where ${\varphi}$ is a trigonometric polynomial given by ${\varphi}(z)$ = ${\sum}^N_{n=-N}a_nz_n(N{\geq}4)$ and satisfies the condition $\bar{a}_N\(\array{a_{-1}\\a_{-2}\\a_{-4}\\{\vdots}\\a_{-N}}\)=a_{-N}\;\(\array{\bar{a}_1\\\bar{a}_2\\\bar{a}_4\\{\vdots}\\\bar{a}_N}\)$. Finally we illustrate the easy applicability of the derived results with a few examples.