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