Right-Existence and LeftExistence of Orthogonality in QuasiBanach Spaces

A class of new generalized orthogonality of quasiBanach spaces is given in this paper. It is a generalization of orthogonality. First, the relation of orthogonality and linear functional are introduced. At the same time, a necessary and sufficient condition of orthogonality in quasiBanach spaces is given. Namely, let X be a quasiBanach spaces on * is equivalent to x⊥H. The sufficient conditions of rightexistence and leftexistence of orthogonality are discussed. Finally, two examples which show that rightexistence of orthogonality in quasiBanach spaces does not exist for all elements are given.(* Indicates a formula, please see the full text)