Abstract
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:
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(1)
(f 1+f 2)(x)=f 1(x)+f 2(x)
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(2)
(λf 1)(x)=λf 1(x); and
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(3)
(f 1 f 2)(x)=f 1(x)f 2(x)
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© 1998 Springer Science+Business Media New York
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Douglas, R.G. (1998). Banach Spaces. In: Banach Algebra Techniques in Operator Theory. Graduate Texts in Mathematics, vol 179. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1656-8_1
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DOI: https://doi.org/10.1007/978-1-4612-1656-8_1
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