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A geometric constant for quantifying the differences between approximate orthogonality types
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DOI：10.1007/s00010-026-01295-5.png)
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Abstract
En 中文
In this paper, we introduce and study a new geometric constant D-epsilon(X) (epsilon is an element of [0, 1)) to measure the difference between approximate isosceles orthogonality and approximate Birkhoff-James orthogonality in real normed linear spaces (X, ||center dot||). A characterization of inner product spaces is provided in terms of the constant D-epsilon(X ). From the inequality concerning approximate isosceles orthogonality, we obtain both lower and upper bounds for D-epsilon(X ). More precisely, we show that & euro; + 2( root 2(1-& euro;) - 1) <= D epsilon(X) <= 1
for all epsilon + (0, 2(root 2 - 1). We further demonstrate that the derived lower bound for D epsilon(X) is sharp.
for all epsilon + (0, 2(root 2 - 1). We further demonstrate that the derived lower bound for D epsilon(X) is sharp.
Keywords:
Approximate Birkhoff-James orthogonality
Approximate isosceles orthogonality
Geometric constant
Inner product spaces