科研之友
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摘要
In this paper, linear epsilon-orthogonality preserving mappings are studied. We define (epsilon) over cap (T) as the smallest epsilon for which T is epsilon-orthogonality preserving, and then derive an exact formula for (epsilon) over cap (T) in terms of parallel to Th parallel to and the minimum modulus m (T) of T. We see that epsilon-orthogonality preserving mappings (for some epsilon < 1) are exactly the operators that are bounded from below. We improve an upper bound in the stability equation given in [7, Theorem 2.3], which was thought to be sharp.
