Weak $A$-frames and weak $A$-semi-frames

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Constructive Mathematical Analysis
Volume:4 Issue:1
Weak $A$-frames and weak $A$-semi-frames

Weak $A$-frames and weak $A$-semi-frames

Authors : Jean Pierre ANTOINE, Giorgia BELLOMONTE, Camillo TRAPANI

Pages : 104-118

Doi:10.33205/cma.835582

View : 20 | Download : 7

Publication Date : 2021-03-01

Article Type : Research Paper

Abstract :After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a weak lower $A$-semi-frame and we study its properties. In particular, we compare it with that of lower atomic systems, introduced in insert ignore into journalissuearticles values(GB);. We discuss duality properties and we suggest several possible definitions for weak $A$-upper semi-frames. Concrete examples are presented.
Keywords : A frames, weak upper and lower, A semi frames, lower atomic systems, G duality

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