Spectral property of upper triangular relation matrices
Yanyan Du, Junjie Huang · Linear and Multilinear Algebra · 2020
Let H and K be infinite dimensional separable Hilbert spaces. For A∈LR(H), B∈LR(K) and C∈LR(K,H), we denote by MC=AC0B the upper triangular relation matrix. In this paper, the sets ⋂C∈CM(K,H)σ(MC), ⋂C∈LR(K,H)σ1(MC) and ⋂C∈B(K,H)σ2(MC) are characterized, where σ1∈{σp,σr,σc} and σ2∈{σ,σp,σr,σc}. Moreover, the relationship between σ(MC), σ(A) and σ(B) is described for given relations A∈BCR(H), B∈BCR(K) and C∈BR(K,H) under the local spectral theory.