On sequence spaces for Fr\'echet frames
Stevan Pilipovi\'c, Diana T. Stoeva

TL;DR
This paper investigates the construction of specialized sequence spaces to establish frame structures, such as Banach and Fréchet frames, for Banach and Fréchet spaces, enhancing understanding of their functional analysis properties.
Contribution
It introduces a method to construct sequence spaces that serve as frames for Banach and Fréchet spaces, extending the theory of frames in functional analysis.
Findings
Constructed sequence spaces serve as frames for Banach and Fréchet spaces.
Established conditions for $ ilde{ heta}$-frames and Banach frames.
Extended frame theory to Fréchet spaces.
Abstract
We analyze the construction of a sequence space , resp. a sequence of sequence spaces, in order to have as a -frame or Banach frame for a Banach space , resp. pre--frame or -frame for a Fr\'echet space , where is a sequence of Banach spaces.
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Taxonomy
TopicsMathematical Analysis and Transform Methods
