Journal of Operator Theory

Volume 67, Issue 1, Winter 2012 pp. 21-31.

An additive invariant on the vector-valued Hardy space over the ball

Authors: Guozheng Cheng
Author institution: School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, 325035, China

Summary: This paper concerns an additive invariant on any invariant subspaces of the vector-valued Hardy space over the ball, which is an analogous version of the Arveson's curvature invariant on the symmetric Fock space. Inspired by Fang's work, we prove that this invariant equals to the fiber dimension of the invariant subspace.

Keywords: Hardy space, curvature invariant, Samuel multiplicity, fiber dimension

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