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- W4317361162 abstract "In this chapter we plunge into the non-linear aspects of the theory of twisted sums. One of the objectives of this chapter is to provide the reader with practical ways to construct non-trivial exact sequences $0 longrightarrow Y longrightarrow cdot longrightarrow X longrightarrow 0$ when only the spaces $Y$ and $X$ are known. The central idea here is that such exact sequences correspond to a certain type of non-linear map called a quasilinear map $Phi: X longrightarrow Y$. The chapter has been organised so that the reader can reach at an early stage a number of important applications. The topics covered include finding pairs of quasi-Banach spaces $X, Y$ such that all exact sequences $0 longrightarrow Y longrightarrow cdot longrightarrow X longrightarrow 0$ split, natural representations for the functor $operatorname{Ext}$, getting valuable insight into the structure of exact sequences and twisted sum spaces, a duality theory for exact sequences of Banach spaces (including a non-linear Hahn-Banach theorem), uniform boundedness principles for exact sequences leading to a local theory for exact sequences, homological properties of the spaces $ell_p$ and $L_p$, type of twisted sums, $mathscr K$-spaces and the Kalton-Peck maps." @default.
- W4317361162 created "2023-01-19" @default.
- W4317361162 date "2023-01-31" @default.
- W4317361162 modified "2023-09-27" @default.
- W4317361162 title "Quasilinear Maps" @default.
- W4317361162 doi "https://doi.org/10.1017/9781108778312.005" @default.
- W4317361162 hasPublicationYear "2023" @default.
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