Artículos

Abstract

ber that a closed subspace M of a real Banach space X is said to be an L2- summand subspace if there exists another closed subspace N of X verifying X = (M ® N)2 (that is, ¡m + n||2 = ||m||2 + ||n||2 for every m e M and every n g N.) The linear projection t?m of X onto M that fixes the elements of M and maps the elements of N to {0} is called the L2-summand projection of X onto M. For a wider perspective about L2-summand subspaces, see [1], [2], and [3]. A vector e of a real Banach space X is an L2-summand vector if Re is an L2- summand subspace. Furthermore, if e A 0 then there exists a functional e* in X*, which is called the L2-summand functional of e, such that ||e*|| = ||e||—1, e* (e) = 1, and 7TRe G) = e* (a:) e for every x £ X. The set of all L2-summand vectors of A' will be denoted by Lx- For a wider perspective about L2-summand vectors, see [1]. Let us recall two relevant results about L2-summand vectors