A family of commuting contraction semigroups on l1(N){l}^{1}\left({\mathbb{N}}) and l∞(N){l}^{∞ }\left({\mathbb{N}}) - Nieznaj Ernest (Open Mathematics, 2025)
A family of commuting contraction semigroups (Pn(t))n∈N{\left(P_{n}\left(t))}_{n\in {\mathbb{N}}}, defined on l1(N){l}^{1}\left({\mathbb{N}}), is presented. For this family, the product semigroup ∏n=1∞Pn(t){\prod }_{n=1}^{∞ }{P}_{n}\left(t) exists and has bounded generator. The infinite product of the corresponding family of adjoint semigroups (Pn∗(t))n∈N{\left(P_{n}^{* }\left(t))}_{n\in {\mathbb{N}}}, defined on l∞(N){l}^{∞ }\left({\mathbb{N}}), also exists and its generator is bounded. Explicit formulae for these generators are also given.