Research

Journal of Inequalities and Applications

, 2012:196

Open Access This content is freely available online to anyone, anywhere at any time.

Bochner pg-frames

  • Mohammad H FaroughiAffiliated withDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of TabrizIslamic Azad University-Shabestar Branch
  • , Morteza RahmaniAffiliated withDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz Email author 

Abstract

In this paper we introduce the concept of Bochner pg-frames for Banach spaces. We characterize the Bochner pg-frames and specify the optimal bounds of a Bochner pg-frame. Then we define a Bochner qg-Riesz basis and verify the relations between Bochner pg-frames and Bochner qg-Riesz bases. Finally, we discuss the perturbation of Bochner pg-frames.

MSC: 42C15, 46G10.

Keywords

Banach space Hilbert space frame Bochner measurable Bochner pg-frame Bochner pg-Bessel family Bochner qg-Riesz basis