Approximate spectral cosynthesis in the harmonically weighted Dirichlet spaces

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Hacettepe Journal of Mathematics and Statistics
Volume:52 Issue:3
Approximate spectral cosynthesis in the harmonically weighted Dirichlet spaces

Approximate spectral cosynthesis in the harmonically weighted Dirichlet spaces

Pages : 721-728

View : 157 | Download : 207

Publication Date : 2023-05-30

Article Type : Research Paper

Abstract :For a finite positive Borel measure $\\mu$ on the unit circle, let $\\mathcal{D}insert ignore into journalissuearticles values(\\mu);$ be the associated harmonically weighted Dirichlet space. A shift invariant subspace $\\mathcal{M}$ recognizes strong approximate spectral cosynthesis if there exists a sequence of shift invariant subspaces $\\mathcal{M}_k$, with finite codimension, such that the orthogonal projections onto $\\mathcal{M}_k$ converge in the strong operator topology to the orthogonal projection onto $\\mathcal{M}$. If $\\mu$ is a finite sum of atoms, then we show that shift invariant subspaces of $\\mathcal{D}insert ignore into journalissuearticles values(\\mu);$ admit strong approximate spectral cosynthesis.
Keywords : weighted Dirichlet spaces, invariant subspaces, strong approximate spectral cosynthesis

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