Fredholm spectrum and growth of cohomology groups

• Autorzy: Jörg Eschmeier
• Języki publikacji: EN

Abstrakty

EN

Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let $σ_{F}(T) = σ(T)∖σ_{e}(T)$ be the non-essential spectrum of T. We show that, for each connected component M of the manifold $Reg(σ_{F}(T))$ of all smooth points of $σ_{F}(T)$, there is a number p ∈ {0, ..., n} such that, for each point z ∈ M, the dimensions of the cohomology groups $H^{p}((z - T)^k,E)$ grow at least like the sequence $(k^{d})_{k≥1}$ with d = dim M.

Kategorie tematyczne

• 32C35: Analytic sheaves and cohomology groups
• 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincar\'e series
• 47A53: (Semi-) Fredholm operators; index theories
• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 186
• Numer: 3
• Strony: 237-249

Daty

wydano

2008

Twórcy

autor

Jörg Eschmeier

• Fachrichtung Mathematik, Universität des Saarlandes, Postfach 15 11 50, D-66041 Saarbrücken, Germany

Identyfikatory

DOI

10.4064/sm186-3-3