Spectral Bundles

Details Spectral Bundles Spectral Bundles

2009-06-16

arxiv.org/abs/0906.2953v2

Mathematics

Functional Analysis

115 pages

Scientific paper

In this work I will construct certain general bundles $<\mathfrak{M},\rho,X>$ and $<\mathfrak{B},\eta,X>$ of Hausdorff locally convex spaces associated to a given Banach bundle $<\mathfrak{E},\pi,X>$. Then I will present conditions ensuring the existence of bounded selections $\mathcal{U}\in \Gamma^{x_{\infty}}(\rho)$ and $\mathcal{P}\in \Gamma^{x_{\infty}}(\eta)$ both continuous at a point $x_{\infty}\in X$, such that $\mathcal{U}(x)$ is a $C_{0}-$semigroup of contractions on $\mathfrak{E}_{x}$ and $\mathcal{P}(x)$ is a spectral projector of the infinitesimal generator of the semigroup $\mathcal{U}(x)$, for every $x\in X$.

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