Fredholm spectrum and growth of cohomology groups

Jörg Eschmeier

Jörg Eschmeier

Studia Mathematica, Tome 187 (2008), p. 237-249 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $R e g (σ_{F} (T))$ 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 ${(k^{d})}_{k \geq 1}$ with d = dim M.

Publié le : 2008-01-01

Zbl 1140.47004

EUDML-ID : urn:eudml:doc:284792

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     author = {J\"org Eschmeier},
     title = {Fredholm spectrum and growth of cohomology groups},
     journal = {Studia Mathematica},
     volume = {187},
     year = {2008},
     pages = {237-249},
     zbl = {1140.47004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-3-3}
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Jörg Eschmeier. Fredholm spectrum and growth of cohomology groups. Studia Mathematica, Tome 187 (2008) pp. 237-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-3-3/