A Finite Multiplicity Helson-Lowdenslager-De Branges Theorem

2009/10/28 by Sneh Lata, Lata, Sneh, Meghna Mittal +3
Mathematics · #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.0910.5416

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 L²(\mathbbT;ℂⁿ), where \mathbbT is the unit circle, by characterizing the invariant subspaces of Sⁿ on scalar valued L^p (0

Citations

• On two problems concerning linear transformations in hilbert space

Related

• Helson-Lowdenslager and de Branges type theorems in the setting of continuous rotationally symmetric norms
• Contractively embedded invariant subspaces
• Conjugations in L² and their invariants
• Lax-Halmos Type Theorems in H^p Spaces
• Doubly invariant subspaces of the Besicovitch space