Fredholm spectrum and growth of cohomology groups

Jörg Eschmeier. "Fredholm spectrum and growth of cohomology groups." Studia Mathematica 186.3 (2008): 237-249. <http://eudml.org/doc/284792>.

@article{JörgEschmeier2008,
abstract = {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.},
author = {Jörg Eschmeier},
journal = {Studia Mathematica},
keywords = {Fredholm spectrum; cohomology groups; Hilbert–Samuel polynomial},
language = {eng},
number = {3},
pages = {237-249},
title = {Fredholm spectrum and growth of cohomology groups},
url = {http://eudml.org/doc/284792},
volume = {186},
year = {2008},
}

TY - JOUR
AU - Jörg Eschmeier
TI - Fredholm spectrum and growth of cohomology groups
JO - Studia Mathematica
PY - 2008
VL - 186
IS - 3
SP - 237
EP - 249
AB - 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.
LA - eng
KW - Fredholm spectrum; cohomology groups; Hilbert–Samuel polynomial
UR - http://eudml.org/doc/284792
ER -