Orthogonality in \ℓ_p-spaces and its bearing on ordered Banach\n spaces

2012/11/30 by Anil Kumar Karn, Karn, Anil Kumar
Computer Science · Mathematics · #47B60 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Optimization and Variational Analysis #Primary: 46B40 #Secondary: 46B45

paper · pdf · doi:10.48550/arxiv.1212.0054

openalex publication_date 2012/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of p-orthogonality in a general Banach space 1 \≤ p\n\≤ \∞. We use this concept to characterize \ℓ_p-spaces among Banach\nspaces and also among complete order smooth p-normed spaces. We further\nintroduce a notion of p-orthogonal decomposition in order smooth p-normed\nspaces. We prove that if the \∞-orthogonal decomposition holds in an\norder smooth \∞-normed space, then the 1-orthogonal decomposition holds\nin the dual space. We also give an example to show that the above said\ndecomposition may not be unique.\n

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