谱意义下的非交换Hardy空间

摘要

ftgt2G是群G作用在VNAM上的*自同构的u001b-弱连续的表示，满足u001cu000et=u001c；t2G.对1u0014p<1，ftgt2G可以延拓到非交换Lp空间上.基于谱子空间理论,讨论了非交换Hardy空间Hp().%Let {αt}t∈G be a σ-weakly continuous representations of group G as ∗-automorphisms of von Neumann algebra M such thatτ◦αt=τ,t∈G. For 1≤p<∞, we extend{αt}t∈G to Lp(M) which be a non-commutative Lp-space and investigate the noncommutative Hardy space Hp(α) based on the theory of spectral subspace.