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arXiv · 1409.7781

A note on linear approximately orthogonality preserving mappings

Ye Zhang·Yanni Chen·Don Hadwin·Liang Kong
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Abstract

In this paper, linear $\varepsilon$-orthogonality preserving mappings are studied. We define $\hat{\varepsilon}\left(T\right) $ as the smallest $\varepsilon$ for which $T$ is $\varepsilon$-orthogonality preserving, and then derive an exact formula for $\hat{\varepsilon}\left( T\right) $ in terms of $\left \Vert T\right \Vert $ and the minimum modulus $m\left( T\right) $ of $T$. We see that $\varepsilon$-orthogonality preserving mappings (for some $\varepsilon<1$) are exactly the operators that are bounded from below. We improve an upper bounded in the stability equation given in [7, Theorem 2.3], which was thought to be sharp.

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Ye Zhang, Yanni Chen, Don Hadwin, Liang Kong. 2014-09-27. A note on linear approximately orthogonality preserving mappings. https://arxiv.org/abs/1409.7781

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