On the left spectra of 2×2 operator matrices
Li Yuan · 2007
Let MX=(■) be a 2×2 operator matrix acting on the Hilbert space HK. In this paper, the sets ∩X∈B(H,K)σl(MX) and ∩X∈B(H,K)σr(MX), are characterized, for given A,B and C, where R(C) is closed, σl(T) and σr(T) denote the left spectrum and the right spectrum of an operator T, respectively. By using the operator matrix, the above sets are studied. The sets ∩X∈B(H,K)σl(MX) and ∩X∈B(H,K)σr(MX) is characterized completely, when R(C) is closed. The formula is interesting in 2×2 operator matrices. It can be used to obtain some known conclusions.