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This paper mainly concerns defect operators for submodules of the Hilbert module H 2 d on the unit ball. The defect operator carries key information about operator theory and structure of submodules. For graded submodules we investigate when such submodules belong to Schatten class L. Furthermore, it is shown that a submodule of H 2 d with finite rank has necessarily finite codimension. This implies an a‰rmative solution for a problem of Arveson.

Defect operators for submodules of H[2][d]