On closed subspaces of grand lebesgue spaces

We prove a generalized version of a theorem of Grothendieck over finite measure space. We prove a closed subspace of grand Lebesgue space that consist of functions of L  must be finite dimensional. By using embeddings of Banach spaces ( ) ( ) ) , p p L L   and ( ) 2 L  we work inside space ( ) 2 L  . Then we take advantage of many useful properties of Hilbert space.