Journal of Operator Theory
Volume 78, Issue 1, Summer 2017 pp. 21-43.
Cowen-Douglas tuples and fiber dimensions
Authors:
Jorg Eschmeier (1) and Sebastian
Langendorfer (2)
Author institution: (1) FR Mathematik, Universitat des Saarlandes,
Saarbrucken, 66041, Germany
(2) FR Mathematik, Universitat des Saarlandes,
Saarbrucken, 66041, Germany
Summary: Let $T \in L(X)^n$ be a Cowen--Douglas tuple on a
Banach space $X$. We use
functional representations of $T$
to associate with each $T$-invariant subspace $Y\subset X$ an integer called
the fiber dimension
$\mathrm{fd}(Y)$ of $Y$.
Among other results we prove a limit formula for the fiber dimension, show
that it is invariant under
suitable changes of $Y$ and deduce
a dimension formula for pairs of homogeneous invariant subspaces of graded
Cowen--Douglas tuples on Hilbert spaces.
DOI: http://dx.doi.org/10.7900/jot.2016may04.2134
Keywords: Cowen-Douglas tuples, fiber dimension, Samuel
multiplicity, holomorphic model spaces
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