On Generalized Quadratic Operators
Hong-Ke Du · Acta Analysis Functionalis Applicata · 2007
Let B(H) denote the set of all bounded linear operators on a Hilbert space H. A∈B(H) is said to be generalized quadratic operator if A satisfies AP=PA=A and the quadratic equation A2=αA+βP, where α, β∈C and P∈B(H) is nonzero idempotent. Let L(P) denote the set of generalized quadratic operators with respect to an idempotent P. In this note, using the technique of operator theory, the spectrum and the group inverse of L(P) have been studied. This extends the conclusions of R. W. Farebrother and G. Trenkler.