ZEMALI, Raounek2024-09-202024-09-202024-06-08http//localhost:8080/jspui/handle/123456789/11909Theobjective of this memory is to study the orthogonality in Banch space, So we will study the orthogonality in different spaces, inC1 classe, L1(B(H)) and B(H), such that B(H) is the algebra of all boundedlinear operators in Hilbert space H. we begin first by the global minimum and orthogonality in C1 class, in the next chapter we will study Birkhof-Jmaes orthogonality in L1(B(H)), Finally we will see the definition of Birkhof-James orthogonality in B(H).enThe Orthogonality, B(H)Thesis