ISOMETRIC WEIGHTED COMPOSITION OPERATORS ON THE FOCK SPACE OF ℂ^N

Abstract

Abstract. This paper gives complete characterization for isometric weighted composition operators on the Fock space of C N . The main result shows that an isometric weighted composition operator on the Fock space of C N is a unitary operator.

Complex symmetric weighted composition operators on the Fock space in several variables

“…Note added in the proof-reading. A recent work by L. Zhao [19] appears to have a characterization for isometric linear weighted composition operators on F(C n ).…”

Binormal and complex symmetric weighted composition operators on the Fock Space over $\mathbb{C}$

“…Suppose that C ϕ is binormal, then by equating ( 9) and ( 10), we get e |b| 2 (a+1)+bw(a|a| 2 +1)+z(|a| 4 w+|a| 2 b+ab) = e |b| 2 (a+1)+bw(|a| 2 +a) e z(|a| 4 w+a|a| 2 b+b) (11) for z, w ∈ C. Taking z = w = 0 in (11), we get…”

“…In [10], L. Zhao characterized unitary weighted composition operators and their spectrum on the Fock space over C n . In [11,12], L. Zhao respectively studied isometric weighted composition operators and bounded invertible weighted composition operators on the Fock space over C n . In [9], T. Le investigated boundedness and compactness of weighted composition operators on F 2 using much simpler characterization than the one in [5].…”

Complex symmetry & weighted composition operators on fock spaces

“…Note that in [18] a description of all isometric weighted composition operators on F 2 (C) is also given. Recently, some of these results have been generalized to the case of higher dimensions in [30].…”