Titlebook: An Introductory Course in Functional Analysis; Adam Bowers,Nigel J. Kalton Textbook 2014 Springer Science+Business Media, LLC, part of Spr

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https://doi.org/10.1007/978-1-4419-8342-8ourselves to considering complex Banach spaces, which will allow us to make use of powerful theorems from complex analysis. (For a brief review of results from complex analysis, see Sect. B.2 in the appendix.)

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The General Theory of Atmospheric TurbulenceSeveral theorems in functional analysis have been labeled as “the Hahn–Banach Theorem.” At the heart of all of them is what we call here the Hahn–Banach Extension Theorem, given in Theorem 3.4, below. This theorem is at the foundation of modern functional analysis, and its use is so pervasive that its importance cannot be overstated.

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https://doi.org/10.1007/978-3-211-78777-9Suppose . is a vector space (over . or .) and let . be a linear operator. Let us recall some basic definitions from linear algebra. The . (or .) of . is the subspace of . given by .. The . (or .) of . is given by .. We say that . is an . of . if . and there exists some scalar λ (called an .) such that ..

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Familial Models for Count Data,In this chapter, we will consider the . for compact hermitian operators on a Hilbert space.

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Compact Operators and Fredholm Theory,Suppose . is a vector space (over . or .) and let . be a linear operator. Let us recall some basic definitions from linear algebra. The . (or .) of . is the subspace of . given by .. The . (or .) of . is given by .. We say that . is an . of . if . and there exists some scalar λ (called an .) such that ..