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Right-Existence and LeftExistence of Orthogonality in QuasiBanach SpacesKeywords: quasiBanach space , orthogonality , hyperplane , rightexistence , leftexistence Abstract: A class of new generalized orthogonality of quasiBanach 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 quasiBanach spaces is given. Namely, let X be a quasiBanach spaces on * is equivalent to x⊥H. The sufficient conditions of rightexistence and leftexistence of orthogonality are discussed. Finally, two examples which show that rightexistence of orthogonality in quasiBanach spaces does not exist for all elements are given.(* Indicates a formula, please see the full text)
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