Linear sums of two composition operators on the Fock space. (English) Zbl 1190.47026
Summary: 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, the cancelation phenomenon is not possible on the Fock space, in contrast to what has been known on other well-known function spaces over the unit disk. We also show analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators, the investigation is left open.
MSC:
| 47B33 | Linear composition operators |
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 46E20 | Hilbert spaces of continuous, differentiable or analytic functions |
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
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