Vol. 5, No. 3, 2012

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Bochner $(p,Y)$-operator frames

Mohammad Hasan Faroughi, Reza Ahmadi and Morteza Rahmani

Vol. 5 (2012), No. 3, 283–293
Abstract

Using the concepts of Bochner measurability and Bochner space, we introduce a continuous version of (p,Y )-operator frames for a Banach space. We also define independent Bochner (p,Y )-operator frames for a Banach space and discuss some properties of Bochner (p,Y )-operator frames.

Keywords
Bochner $(p,Y)$-operator frame, Bochner measurability, Bochner space, Radon–Nikodym property
Mathematical Subject Classification 2010
Primary: 42C15, 46C05
Milestones
Received: 16 April 2011
Accepted: 21 January 2012
Published: 14 April 2013

Communicated by David R. Larson
Authors
Mohammad Hasan Faroughi
Department of Pure Mathematics
Faculty of Mathematical Science
University of Tabriz
29 Bahman Street
Tabriz 5166614766
Iran
Reza Ahmadi
Department of Pure Mathematics
Faculty of Mathematical Science
University of Tabriz
29 Bahman Street
Tabriz 5166614766
Iran
Morteza Rahmani
Department of Pure Mathematics
Faculty of Mathematical Science
University of Tabriz
29 Bahman Street
Tabriz 5166614766
Iran
Department of Mathematics
Ilam University
P.O. Box 69315516
Ilam
Iran