Linear Operators on Banach Spaces

Toka Diagana
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Toka Diagana: Howard University, Department of Mathematics

Chapter Chapter 2 in Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, 2013, pp 43-77 from Springer

Abstract: Abstract Let $$(\mathcal{X},\|\cdot \|)$$ and $$(\mathcal{Y},\|\cdot \|_{1})$$ be two Banach spaces over the same field $$\mathbb{F}$$ . A mapping $$A: D(A) \subset \mathcal{X} \rightarrow \mathcal{Y}$$ satisfying $$\displaystyle{A(\alpha x +\beta y) =\alpha Ax +\beta Ay}$$ for all x,y∈D(A) and $$\alpha,\beta \in \mathbb{F}$$ , is called a linear operator or a linear transformation.

Keywords: Sectorial Linear Operator; Diagana; Family Development; Real Interpolation Space; Acquistapace Terreni Conditions (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-319-00849-3_2

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