Frames, Operators and related Topics, 15. - 19. July 2024


1) Banach frames establish an embedding of a given function spaces into
a closed and complemented subspace of a corresponding sequence space.
The best way to understand Banach frames is thus via a commutative diagram.

2) The fact that Banach frames should be viewed in the context of families
of Banach spaces instead of individually requires to take care of constants, which are supposed to be valid uniformly over suitable subfamilies. This will be illustrated in the context of the Banach Gelfand Triple $(S_0,L^2,S*_0)$,
consisting of Feichtinger's algebra, the Hilbert space $L^2$ and the dual space of ``mild distributions''.

3) In the Hilbert spaces context the question of enumeration of the elements is usually not even mentioned. While unconditional convergence is automatic in this case it is not at all obvious for Banach frames and may raise interesting questions.

As time permits concrete illustrative examples will be provided in the talk, mostly from the area of Gabor Analysis.