Banach Spaces L p

Carlos S. Kubrusly
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Carlos S. Kubrusly: Catholic University of Rio de Janeiro, Electrical Engineering Department

Chapter 5 in Essentials of Measure Theory, 2015, pp 71-87 from Springer

Abstract: Abstract A topology to equip the linear space $$\mathcal{L}(X,\mathcal{X},\mu )$$ which will turn it into a Banach space is investigated in this chapter. Section 5.1 summarizes the basics on normed spaces that will be required in Chapter 5 (as well as in parts of Chapters and 6 , 10 , and 12 ). We assume the reader has been introduced to linear spaces (or vector space) before — see e.g., Lemma 4.5.

Keywords: Banach Space; Equivalence Class; Linear Space; Normed Space; Measure Space (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-22506-7_5

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