Hardy-type sequence spaces and Cesaro frames

Cesaro averaging is used in conjunction with Hardy space andHilbert space theory to realize certain types of convergence.In Chapter 1, we study certain Hardy-type sequence spaces, which are analogues ofell-infinity and c_0, respectively. We show that the Mazurproduct is not onto, which provides a new solution of Mazur's Problem 8 in the Scottish Book. We present corollaries for spaces defined via weighted ell-p seminorms and for c_0.In Chapter 2, we study the application of Cesaro operators onBessel sequences to realize a weak version of frame reconstructionin Hilbert space. Conditions for reconstruction via Markuschevichbases that are certain linear combinations of orthonormal basisvectors are given