Speaker: James Tanis (UMD)

Title: Frame theory and the Kaczmarz algorithm


In 2001 Kwapien and Mycielski generalized the classical Kaczmarz algorithm to Hilbert space and Banach space. Moreover, they introduced the notion of an effective sequence in this context, which shall be a central concept. In 2006 Szwarc and Haller exploited the additional structure of the Kaczmarz algorithm in Hilbert space, and much of the talk shall focus on their work. We characterize effective sequences by partial isometries and show that effective sequences characterize infinite dimensional 1-tight frames. Finally, we extend part of their work to the context of not necessarily tight frames, Riesz bases and orthonormal bases.