Trace conditions for regular spectral behavior of vector-valued analytic functions

✍ Scribed by H. Bart; T. Ehrhardt; B. Silbermann

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 261 KB
• Volume: 430
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.11.004

✦ Synopsis

Idempotent Annihilating family of idempotents Resolving family of traces Integer combination of idempotents

A new class of Banach algebra valued functions is identified for which the logarithmic residue with respect to a Cauchy domain vanishes (if and) only if the functions take invertible values in . Trace conditions and the extraction of elementary factors of the type ep + (λ -α)p play an important role. The class contains the Fredholm operator valued functions and the Banach algebra valued functions possessing a simply meromorphic resolvent as special instances. An example is given to show that new ground is covered and a long standing open problem is discussed from a fresh angle.