Titlebook: An Introduction to Banach Space Theory; Robert E. Megginson Textbook 1998 Springer Science+Business Media New York 1998 Banach Space.Smoot

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,Implikationen für die Marketing-Forschung,dean 2- or 3-space. However, closed unit balls are sometimes not so nicely shaped. Consider, for example, the closed unit balls of real ℓ. and ℓ.. Neither is round by any of the usual meanings of that word, since their boundaries, which is to say the unit spheres of the spaces, are each composed of

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https://doi.org/10.1007/978-1-4612-0603-3Banach Space; Smooth function; compactness; differential equation; functional analysis; measure

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978-1-4612-6835-2Springer Science+Business Media New York 1998

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Mendicant

Basic Concepts,t twelve sections of this chapter, with the exception of that of Section 1.5, is used extensively throughout the rest of this book. Section 1.13, though containing material that is very important in modern Banach space theory, is optional in the sense that the few results and exercises in the rest o

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Schauder Bases,ry linear operator from a finite-dimensional normed space . into any normed space . is bounded. A careful examination of the proof of that theorem shows that it essentially amounts to demonstrating that if .,…, . is a vector space basis for ., then each of the linear “coordinate functionals”α. + … +

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Rotundity and Smoothness,dean 2- or 3-space. However, closed unit balls are sometimes not so nicely shaped. Consider, for example, the closed unit balls of real ℓ. and ℓ.. Neither is round by any of the usual meanings of that word, since their boundaries, which is to say the unit spheres of the spaces, are each composed of