An identity for (delta, epsilon)-approximately orthogonality preserving mappings

作者：Zhang, Ye^*

来源：Linear Algebra and Its Applications, 2018, 554: 358-370.

DOI：10.1016/j.laa.2018.06.001

• Orthogonality preserving mappings
• Approximate orthogonality
• (delta, epsilon)-orthogonality preserving operators
• Minimum modulus

Suppose T is a Hilbert space operator. Given delta is an element of [0, 1), we define (epsilon) over cap (delta) (T) to be the smallest epsilon for which T is (delta, epsilon)-approximately orthogonality preserving, and then obtain an exact formula for (epsilon) over cap (delta) (T) in terms of delta, parallel to T parallel to and the minimum modulus m (T) of T. For two nonzero operators T, S, it follows from the formula that T is ((epsilon) over cap (S), epsilon)-AOP if and only if S is ((epsilon) over cap (T), epsilon)-AOP, where & nbsp;(epsilon) over cap (T) = (epsilon) over cap (0) (T). Finally, we show that an operator T is (delta, epsilon)-AOP if and only if there exists a "special" delta-AOP operator S such that TS is epsilon-AOP [Theorem 3.8].

• 出版日期2018-10-1
• 单位陕西师范大学