摘要
For a tuple A = （A1, A2,..., An） of elements in a unital algebra/3 over C, its projective spectrum P（A） or p（A） is the collection of z ∈ Cn, or respectively z ∈ pn-1 such that A（z） = z1A1＋z2A2＋…＋znAn is not invertible in/3. The first half of this paper proves that if/3 is Banach then the resolvent set PC（A） consists of domains of holomorphy. The second half computes the projective spectrum for the generating vectors of a Clifford algebra. The Chern character of an associated kernel bundle is shown to be nontrivial.
For a tuple A=(A_1,A_2,…,A_n) of elements in a unital algebra B over C,its projective spectrum P(A) or p(A) is the collection of z∈C^n,or respectively z∈P^(n-1),such that A(z)=z_1A_1+z_2A_2+…+z_nA_n is not invertible in Β.The first half of this paper proves that if B is Banach then the resolvent set P^c(A) consists of domains of holomorphy.The second half computes the projective spectrum for the generating vectors of a Clifford algebra.The Chern character of an associated kernel bundle is shown to be nontrivial.
基金
supported by National Natural Science Foundation of China(Grant No.11101079)and China Scholarship Council
