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A W-transform-based criterion for the existence of bounded extensions of E-operators |
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| Authors: | Caishi Wang Zhiyuan Huang Xiangjun Wang |
| Affiliation: | a Department of Control Science and Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China b School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China c Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China |
| Abstract: | Let Γ(H) be the symmetric Fock space over a Hilbert space H and ε:H→Γ(H) the exponential mapping. By an E-operator we mean an operator defined on ε(H). For an E-operator A, the composition mapping Φ=A°ε is called its W-transform. In this paper, we obtain a criterion based on the W-transform for checking whether or not an E-operator becomes a bounded linear operator on the Fock space. |
| Keywords: | Fock space Exponential vector E-operator W-transform |
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