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- W4244222712 abstract "Abstract 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." @default.
- W4244222712 created "2022-05-12" @default.
- W4244222712 creator A5006497686 @default.
- W4244222712 date "2021-03-09" @default.
- W4244222712 modified "2023-09-25" @default.
- W4244222712 title "Banach Spaces" @default.
- W4244222712 doi "https://doi.org/10.1093/oso/9780198868781.003.0006" @default.
- W4244222712 hasPublicationYear "2021" @default.
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