THE NORMING SET OF A SYMMETRIC n- LINEAR FORM ON THE PLANE WITH A ROTATED SUPREMUM NORM FOR n = 3, 4, 5

초록

Let n is an element of N, n >= 2. An element ( x 1 , ... , x n ) is an element of E n is called a norming point of T is an element of L ( n E ) if parallel to x1 parallel to= 1 parallel to = <middle dot> <middle dot> <middle dot> = parallel to xn parallel to n parallel to = 1 and |T(x1, ( x 1 , ... , xn)| n ) | = parallel to T parallel to, , where L ( n E ) denotes the space of all continuous n-linear forms on E . For T is an element of L ( n E ), we define { } Norm(T) T ) = ( x 1 ,... , x n ) is an element of E n : ( x 1 , ... , x n ) is a norming point of T . Norm(T) T ) is called the norming set of T . Let 0 <= theta <= 4 pi 4 pi and & ell; 2 infinity ,theta = R 2 with the rotated supremum norm { } parallel to(x, ( x, y ) parallel to ( infinity ,theta) = max |x cos theta + y sin theta|, |x sin theta - y cos theta| . In this paper, we characterize the norming set of T is an element of L ( n & ell; 2( infinity ,theta) ). Using this result, we completely describe the norming set of T is an element of L s ( n & ell; 2 (infinity,theta)) infinity ,theta) ) for n = 3, , 4, , 5, where L s ( n & ell; 2( infinity ,theta) ) denotes the space of all continuous symmetric n-linear forms on & ell; 2( infinity ,theta) . We generalizes the results from [9] for n = 3 and theta= = pi 4. .

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