Author/Authors :
Pappas, A Department - School of Technological Applications - Piraeus University of Applied Sciences (Technological Education Institute of Piraeus) - Egaleo - Athens, Greece , Papadopoulos, P Department of Electronics Engineering - School of Technological Applications - Piraeus University of Applied Sciences (Technological Education Institute of Piraeus) - Egaleo - Athens, Greece , Athanasopoulou, L Department - School of Technological Applications - Piraeus University of Applied Sciences (Technological Education Institute of Piraeus) - Egaleo - Athens, Greece
Abstract :
In this paper we will prove that if L is a continuous symmetric n-linear form on a Hilbert space and
bL
is the associated continuous n-homogeneous polynomial, then ǁLǁ = ǁbL
ǁ. For the proof we are
using a classical generalized inequality due to S. Bernstein for entire functions of exponential type.
Furthermore we study the case that if X is a Banach space then we have that
