Abstract

Let T be a linear operator on a Hilbert space H . A method of estimation and calcu+lation of inf{Re( Tx, x)/‖ Tx‖: xϵ H , ‖ x‖ = 1} as well as some other expressions containing two quadratic forms is proposed. This method is based on the Toeplitz- Hausdorff theorem on the convexity of the numerical range of any operator on H .

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