A W-transform-based criterion for the existence of bounded extensions of E-operators

• Published in: Journal of mathematical analysis and applications Vol. 288; no. 2; pp. 397 - 410
• Main Authors: Wang, Caishi, Huang, Zhiyuan, Wang, Xiangjun
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.12.2003; Elsevier
• Subjects: Classical and quantum physics: mechanics and fields; E-operator; Exact sciences and technology; Exponential vector; Fock space; Functional analysis; Functional analytical methods; Mathematical analysis; Mathematics; Operator theory; Physics; Quantum mechanics; Sciences and techniques of general use; W-transform; E-operator; Fock space; Exponential vector; W-transform; Quantum computation; Mathematical analysis; Stochastic calculus; Fréchet analytic mapping; W transform; Bounded operator; E operator; Linear operator; Mathematical physics
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2003.08.049

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.