Approximate spectral cosynthesis in the harmonically weighted Dirichlet spaces

Year 2023, Volume: 52 Issue: 3 , 721 - 728 , 30.05.2023

Faruk Yılmaz

https://doi.org/10.15672/hujms.1171901

https://izlik.org/JA43JH57MT

Abstract

For a finite positive Borel measure $\mu$ on the unit circle, let $\mathcal{D}(\mu)$ 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 $\mathcal{D}(\mu)$ admit strong approximate spectral cosynthesis.

Keywords

weighted Dirichlet spaces , invariant subspaces , strong approximate spectral cosynthesis

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