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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 3

Some characterizations of inner product spacesbased on angle

S.M.S. Nabavi SALES
Pages
626–632
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also speak about a notion of orthogonality concerning it, we call itθ-orthogonality.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A problem in functional analysis that arises naturally is about finding necessary andsufficient conditions for a normed space to be an inner product space.
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Key Findings & Data:Weintroduce a notion of angle between two vectors in a normed space, denoted by$A_θ$(.,.)whereθ̸=kπ2.
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Conclusion & Impact:We also speak about a notion of orthogonality concerning it, we call itθ-orthogonality.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

A problem in functional analysis that arises naturally is about finding necessary andsufficient conditions for a normed space to be an inner product space. By answering thisquestion, mathematicians try to understand the inner product and normed spaces features.In this note, we have discussed this issue and we prove some results concerned with it. Weintroduce a notion of angle between two vectors in a normed space, denoted by$A_θ$(.,.)whereθ̸=kπ2. We also speak about a notion of orthogonality concerning it, we call itθ-orthogonality.

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Cite This Article

SALES, S. N. (2022). Some characterizations of inner product spacesbased on angle. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 3, 626–632. https://ajindex.com/articles/529717

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References (1)

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