Article ID Journal Published Year Pages File Type
8897759 Linear Algebra and its Applications 2018 13 Pages PDF
Abstract
Suppose T is a Hilbert space operator. Given δ∈[0,1), we define εˆδ(T) to be the smallest ε for which T is (δ,ε)-approximately orthogonality preserving, and then obtain an exact formula for εˆδ(T) in terms of δ,‖T‖ and the minimum modulus m(T) of T. For two nonzero operators T,S, it follows from the formula that T is (εˆ(S),ε)-AOP if and only if S is (εˆ(T),ε)-AOP, where εˆ(T)=εˆ0(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
,