Derivations, derivatives and chain rules

✍ Scribed by Rajendra Bhatia; Kalyan B. Sinha

• Book ID: 104156648
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 116 KB
• Volume: 302-303
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00084-1

✦ Synopsis

For a smooth function f on the space of bounded operators in a Hilbert space, we obtain formulas for the nth order commutator f eY Y Y F F F Y in terms of the Fr echet derivatives h m f e. We illustrate the use of these formulas in obtaining bounds for norms of generalised commutators f e À f f and their higher order analogues.