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Research Paper | Mathematics | India | Volume 3 Issue 7, July 2014 | Rating: 6.7 / 10

A Note on Finite Rank Quadratic Operators

B. Krishna Reddy ^[2] | N. Gopal Reddy

Abstract: 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 ASL (H) is derived.

Keywords: finite rank operator, quadratic operator, numerical range, Hilbert Schmidt quadratic operator, bilinear operator

Edition: Volume 3 Issue 7, July 2014,

Pages: 41 - 43