可解 C~*代数张量积中的交换算子组的联合p-谱和p-指标(英文)

JOINT p-SPECTRUM AND p-INDEX OF n-TUPLES OF COMMUTING OPERATORS IN TENSOR PRODUCTS OF SOLVABLE C~*-ALGEBRAS

本文定义了可解 C~*代数的 p-谱和 p-指标。若 T=(T_1,…,T_n)和 S=(S_1,…,S_n)分别是 A 和 B 中的交换算子组,则对任意 p,等式σ_p(T(?)I,I(?)S)=U(?)σ_i(T)×σ_j(S)成立。并且,若 T 是 i—Tredhlm,S 是 j—Fredholm,则(T(?)I,I(?)S)是p-Fredholm,其中 p=i+j-1,而 Ind_p(T(?)I,I(?)S)=(Ind_iT)。(Ind_jS)。

The joint p-spectrum and p-index of n-tuples of solvable C~*-algebra have been defined.If T=(T_1,…,T_n)and(S_1,…,S_m)are commutingoperators systems in solvable C~*-algebra (?) and (?) respectivly,then theequality σ_p(T(?)I, I(?)S)=(?)σ_i(T)×σ_j(S)hold for any p.Furthermore,if T is i-Fredholm and S is j-Fredholm,then(T(?)I,I(?)S)is p-Fredholm,p=i+j-1,and Ind_p(T(?)I,I(?)S)=(Ind_iT)(?)(Ind_jS).