@article {
author = {Ismailov, Migdad},
title = {On Uncountable Frames and Riesz Bases in Nonseparable Banach Spaces},
journal = {Sahand Communications in Mathematical Analysis},
volume = {19},
number = {2},
pages = {149-170},
year = {2022},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2021.523500.905},
abstract = {Some generalizations of Besselian, Hilbertian systems and frames in nonseparable Banach spaces with respect to some nonseparable Banach space $K$ of systems of scalars are considered in this work. The concepts of uncountable $K$-Bessel, $K$-Hilbert systems, $K$-frames and $K^{*} $-Riesz bases in nonseparable Banach spaces are introduced. Criteria of uncountable $K$-Besselianness, $K$-Hilbertianness for systems, $K$-frames and unconditional $K^{*} $-Riesz basicity are found, and the relationship between them is studied. Unlike before, these new facts about Besselian and Hilbertian systems in Hilbert and Banach spaces are proved without using a conjugate system and, in some cases, a completeness of a system. Examples of $K$-Besselian systems which are not minimal are given. It is proved that every $K$-Hilbertian systems is minimal. The case where $K$ is an space of systems of coefficients of uncountable unconditional basis of some space is also considered.},
keywords = {Nonseparable Banach space,Uncountable unconditional basis,$K$-Bessel and $K$-Hilbert systems,$K$-frames,uncountable unconditional $K$-Riesz bases},
url = {https://scma.maragheh.ac.ir/article_252487.html},
eprint = {https://scma.maragheh.ac.ir/article_252487_22bde7068edb87cf8c0a534e9a8ac4aa.pdf}
}