Part of the Graduate Texts in Mathematics book series (GTM, volume 179)
1.1 We begin by introducing the most representative example of a Banach space. LetXbe a compact Hausdorff space and letC(X)denote the set of continuous complex-valued functions onX.For fiand f2 inC(X)and X a complex number, we define:
(f 1+f 2)(x)=f 1(x)+f 2(x)
(λf 1)(x)=λf 1(x); and
(f 1 f 2)(x)=f 1(x)f 2(x)
KeywordsBanach Space Linear Space Extreme Point Unit Ball Bounded Variation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Science+Business Media New York 1998