A Note on Finite Rank Quadratic Operators
B. Krishna Reddy, N. Gopal Reddy · 2014
The representation result of a finite rank quadratic operator is given. It has been shown that the space FQ(H) of finite rank bounded quadratic operators on a real separable Hilbert space H is equal to the cross spaces L(H) ⊗H and SL(H) ⊗H for a space SL(H) of self-adjoint bonded linear operators on H and the space L(H) of bounded linear operators on H. As an application of the concept of finite rank quadratic operator, the numerical range of an operator A∈SL(H) is derived.