### A Finite Multiplicity Helson-Lowdenslager-De Branges TheoremA Finite Multiplicity Helson-Lowdenslager-De Branges Theorem

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 Author Lata, Sneh ♦ Mittal, Meghna ♦ Singh, Dinesh Source arXiv.org Content type Text File Format PDF Date of Submission 2009-10-28 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Functional Analysis ♦ Mathematics - Complex Variables ♦ 47A15 (Primary) ♦ math Abstract This paper proves two theorems. The first of these simplifies and lends clarity to the previous characterizations of the invariant subspaces of $S$, the operator of multiplication by the coordinate function $z$, on $L^2(\mathbb{T};\mathbb{C}^n)$, where $\mathbb{T}$ is the unit circle, by characterizing the invariant subspaces of $S^n$ on scalar valued $L^p$ (\$0