Schauder Bases

1978 ◽  
Vol 85 (4) ◽  
pp. 256-257
Author(s):  
P. R. Halmos
Keyword(s):  
Schauder Bases

On the equivalence of weak and Schauder bases

1986 ◽  
Vol 46 (5) ◽  
pp. 447-452 ◽  
Author(s):  
Jos� Orihuela
Keyword(s):  
Schauder Bases

Schauder bases and diametrically complete sets with empty interior

2018 ◽  
Vol 463 (2) ◽  
pp. 452-460 ◽  
Author(s):  
Monika Budzyńska ◽  
Aleksandra Grzesik ◽  
Wiesława Kaczor ◽  
Tadeusz Kuczumow
Keyword(s):  
Empty Interior ◽  
Schauder Bases ◽  
Complete Sets

Banach Spaces

2021 ◽  
pp. 245-289
Author(s):  
Adel N. Boules
Keyword(s):  
Banach Spaces ◽  
Uniform Boundedness ◽  
Linear Transformations ◽  
Closed Graph Theorem ◽  
Complemented Subspaces ◽  
Good Account ◽  
Banach Theorem ◽  
Schauder Bases ◽  
Uniform Boundedness Principle ◽  
Adjoint Operators

The first four sections of this chapter form its core and include classical topics such as bounded linear transformations, the open mapping theorem, the closed graph theorem, the uniform boundedness principle, and the Hahn-Banach theorem. The chapter includes a good number of applications of the four fundamental theorems of functional analysis. Sections 6.5 and 6.6 provide a good account of the properties of the spectrum and adjoint operators on Banach spaces. They may be largely bypassed, since the treatment of the corresponding topics for operators on Hilbert spaces in chapter 7 is self-contained. The section on weak topologies is more advanced and may be omitted if a brief introduction is the goal. The chapter is enriched by such topics as the best polynomial approximation, the Hilbert cube, Gelfand’s theorem, Schauder bases, complemented subspaces, and the Banach-Alaoglu theorem.

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