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Orthogonality in locally convex spaces: Two nonlinear generalizations of Neumann's lemma

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Abstract In this note we prove a symmetric version of the Neumann lemma as well as a symmetric version of the Soderlind-Campanato lemma. We establish in this way two partial… Click to show full abstract

Abstract In this note we prove a symmetric version of the Neumann lemma as well as a symmetric version of the Soderlind-Campanato lemma. We establish in this way two partial generalizations of the well-known Casazza-Christenses lemma. This work is related to the Birkhoff-James orthogonality and to the concept of near operators introduced by S. Campanato.

Keywords: two nonlinear; spaces two; orthogonality locally; convex spaces; neumann lemma; locally convex

Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019

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