Banach Spaces

  • Ronald G. Douglas
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:
  1. (1)

    (f 1+f 2)(x)=f 1(x)+f 2(x)

  2. (2)

    f 1)(x)=λf 1(x); and

  3. (3)

    (f 1 f 2)(x)=f 1(x)f 2(x)



Banach Space Linear Space Extreme Point Unit Ball Bounded Variation 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Ronald G. Douglas
    • 1
  1. 1.Department of MathematicsTexas A & M UniversityCollege StationUSA

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