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

Keywords: quasiBanach space , orthogonality , hyperplane , rightexistence , leftexistence

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Abstract:

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)

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