On R-duals and the duality principle in Banach frames

ABSTRACT

In this paper, we derive a connection between the Riesz-dual sequences with respect to a BK-space and framings in Banach spaces. Also, we define the concept of g-framing for Banach spaces and we consider the stability of framings and g-framings. In particular, we give some conditions under which a pair of Riesz-dual sequences to be a g-framing.

KEYWORDS:

• Banach frame
• g-framing
• $X_d$-Riesz basis
• Riesz-dual sequence

2000 MATHEMATICS SUBJECT CLASSICATION:

• Primary: 46B45
• 46B15
• Secondary:42C15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors' work was partially supported by the Science and Research Branch of Islamic Azad University.