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On a class of weighted composition operators on Fock space
Authors: Namita Das
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Abstract
Let $T_{\phi}$ be the Toeplitz operator defined on the Fock space $L_a^2(\mathbb C)$ with symbol $\phi\in L^{\infty}(\mathbb C).$ Let for $\lambda\in \mathbb C,$ $k_{\lambda}(z)=e^{\frac{\bar\lambda z}{2}-\frac{|\lambda|^2}{4}},$ the normalized reproducing kernel at $\lambda$ for the Fock space $L_a^2(\mathbb C)$ and $t_{\alpha}(z)=z-\alpha, z, \alpha\in \mathbb C.$ Define the weighted composition operator $W_{\alpha}$ on $L_a^2(\mathbb C)$ as $(W_{\alpha}f)(z)=k_{\alpha}(z)(f\circ t_{\alpha})(z).$ In this paper we have shown that if $M$ and $H$ are two bounded linear operators from $L_a^2(\mathbb C)$ into itself such that $MT_{\psi}H=T_{\psi\circ t_{\alpha}}$ for all $\psi\in L^{\infty}(\mathbb C),$ then $M$ and $H$ must be constant multiples of the weighted composition operator $W_{\alpha}$ and its adjoint respectively.P.G. Department of Mathematics
Utkal University, Vani Vihar
Bhubaneswar, Orissa, India 751004
E-mail:
Utkal University, Vani Vihar
Bhubaneswar, Orissa, India 751004
E-mail:
Fulltext
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Contents
- On a class of weighted composition operators on Fock space
- Invariant Characteristics of Special Compositions in Weyl Spaces WN
- Interpolating Bézier spline curves with local control
- Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions
- On π-quasigroups of type T1
- Irreducible triangulations of the Möbius band
- On 2-primal Ore extensions over Noetherian Weak σ-rigid rings
- Max-Erlang and Min-Erlang power series distributions as two new families of lifetime distribution
- A semi-isometric isomorphism on a ring of matrices
- Compact Global Attractors of Non-Autonomous Gradient-Like Dynamical Systems
- One new class of cubic systems with maximum number of invariant lines omitted in the classification of J. Llibre and N. Vulpe
