Linear sums of two composition operators on the Fock space

Abstract

Linear sums of two composition operators of the multi-dimensional Fock space are studied. We show that such an operator is bounded only when both composition operators in the sum are bounded. So, cancelation phenomenon is not possible on the Fock space, in contrast to what have been known on other well-known function spaces over the unit disk. We also show the analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators the investigation is left open.

Fock spaces and relative operators

“…2010 年, Choe 等人 [43] 对 Fock 空间上两个复合算子的线性组合进行了研究. 2014 年, Cho [19] 讨 论了复合算子的有限线性组合在 Fock-Sobolev 空间上的特性.…”

Topological Structure of the Space of Composition Operators Between Different Fock Spaces

“…Recently, much progress was made in the study of composition operators on Fock spaces (see, for instance, [5,6,11]). One of the main differences between operators C ϕ on Fock spaces and those on the above-mentioned spaces of holomorphic functions on the unit disc or the unit ball is the lack of bounded holomorphic functions in the Fock space setting.…”

Weighted composition operators between Fock spaces in several variables

“…[20]). From this reason they have been studied intensively in different directions (see, for instance, [1, 2, 11, 14] for Toeplitz operators, [16, 19] for Hankel operators, [5, 12] for Volterra‐type integration operators, [3, 4, 7–9, 13, 18] for (weighted) composition operators).…”