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On the Construction of Sequence Spaces that have Schauder Bases
Canadian Journal of Mathematics, 1966It is known that every Banach space which possesses a Schauder basis is essentially a space of sequences (6, Section 11.4). The primary objectives of this paper are: (1) to illustrate the close connection between sectionally bounded BK spaces and Banach spaces which have a Schauder basis, and (2) to consider some results in these theories in such a way
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The Schauder basis in the solution space of a homogeneous convolution equation
Mathematical Notes, 1995As stated in the title, the author shows that the solution space of a homogeneous convolution equation has a Schauder basis. More precisely, let \(D\) be a convex domain in the complex plane \(C\), and let \(u\) be an analytic functional of \(H^*(D)\) where \(H(D)\) is the space of analytic functions in \(D\) with uniform topology on compact sets of ...
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On Closed Subspaces of Non-Archimedean Nuclear Fréchet Spaces with a Schauder Basis
The Journal of Geometric Analysis, 2013The author continues the study that he started in 2000 about the structure of Fréchet spaces \(E\) over non-Archimedean valued fields. This time he pays attention to closed subspaces of non-Archimedean nuclear Fréchet spaces with a Schauder basis. Let \(\Gamma\) be the family of all non-decreasing unbounded sequences of real positive numbers.
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An endpoint Balian-Low theorem for Schauder bases
Journal of Mathematical Analysis and Applications, 2020Alexander M Powell
exaly
Shrinking and boundedly complete Schauder frames in Fréchet spaces
Journal of Mathematical Analysis and Applications, 2014José Bonet +2 more
exaly
On the Effective Existence of Schauder Bases
Electronic Notes in Theoretical Computer Science, 2008exaly