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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