A Grüss inequality for n-positive linear maps

✍ Scribed by Mohammad Sal Moslehian; Rajna Rajić

• Book ID: 104038408
• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 147 KB
• Volume: 433
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.06.006

✦ Synopsis

Let A be a unital C * -algebra and let Φ : A → B(H) be a unital npositive linear map between C * -algebras for some n 3. We show that

Φ(AB) -Φ(A)Φ(B) Δ(A, || • ||) Δ(B, || • ||)

for all operators A, B ∈ A, where Δ(C, • ) denotes the operator norm distance of C from the scalar operators.