Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897759 | Linear Algebra and its Applications | 2018 | 13 Pages |
Abstract
Suppose T is a Hilbert space operator. Given δâ[0,1), we define εËδ(T) to be the smallest ε for which T is (δ,ε)-approximately orthogonality preserving, and then obtain an exact formula for εËδ(T) in terms of δ,âTâ and the minimum modulus m(T) of T. For two nonzero operators T,S, it follows from the formula that T is (εË(S),ε)-AOP if and only if S is (εË(T),ε)-AOP, where εË(T)=εË0(T). Finally, we show that an operator T is (δ,ε)-AOP if and only if there exists a “special” δ-AOP operator S such that TS is ε-AOP [Theorem 3.8].
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ye Zhang,