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Published in:
1998 | OriginalPaper | Chapter
Banach Spaces
Author : Ronald G. Douglas
Published in: Banach Algebra Techniques in Operator Theory
Publisher: Springer New York
Included in: Professional Book Archive
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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: (1)(f1+f2)(x)=f1(x)+f2(x) (2)(λf1)(x)=λf1(x); and (3)(f1f2)(x)=f1(x)f2(x)