Riesz Spaces, Volume 2
While Volume I (by W.A.J. Luxemburg and A.C. Zaanen, NHML Volume 1, 1971) is devoted to the algebraic aspects of the theory, this volume emphasizes the analytical theory of Riesz spaces and operators between these spaces. Though the numbering of chapters continues on from the first volume, this does not imply that everything covered in Volume I is required for this volume, however the two volumes are to some extent complementary.
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CHAPTER 11 PRIME IDEAL EXTENSION
CHAPTER 12 ORDER BOUNDED OPERATORS
CHAPTER 13 KERNEL OPERATORS
CHAPTER 14 NORMED RIESZ SPACES
CHAPTER 15 ORDER CONTINUOUS NORMS
CHAPTER 16 EMBEDDING IN BIDUALS
CHAPTER 17 ABSTRACT Lp SPACES
absolute kernel operator algebra AM—compact Archimedean Archimedean Riesz space assume Banach lattice band Boolean ring bounded sets carrier compact complete Riesz space condition Dedekind complete defined denoted directed sets disjoint complement disjoint sequence distributive lattice equivalent everywhere EXERCISE exists a sequence exists an element f E L f-algebra finite follows Furthermore Hence holds hypothesis implies L+iL last theorem lemma linear subspace mapping measure space minimal prime ideal non—empty norm bounded norm closed normed Riesz space Note null o—order continuous operator norm order bounded operator order continuous norm order dense order dual Orth(L orthomorphism p(un positive elements positive linear functional positive operator principal ideal projection property proof proper prime ideal prove real numbers Riesz norm Riesz seminorm Riesz subspace satisfying semi—compact Show Similarly strictly positive subset supremum topology vector space weak Fatou property weak unit zero