Summability Through Functional Analysis (Google eBook)
Summability is an extremely fruitful area for the application of functional analysis; this volume could be used as a source for such applications. Those parts of summability which only have ``hard'' (classical) proofs are omitted; the theorems given all have ``soft'' (functional analytic) proofs.
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CHAPTER 12 DISTINGUISHED SUBSPACES OF MATRIX DOMAINS
CHAPTER 13 DISTINGUISHED SUBSPACES OF cA
CHAPTER 14 THE FUNCTIONAL μ
CHAPTER 15 THE SUBSPACE P
CHAPTER 16 SEQUENTIAL COMPLETENESS AND SEPARABILITY
CHAPTER 17 MAPS OF BANACH SPACES
CHAPTER 18 ALGEBRA
CHAPTER 19 MISCELLANY
Abel's identity absolutely convex Banach algebra Banach space Banach-Steinhaus theorem bounded divergent sequences bounded sequences bounded set Bx)n Cauchy closed subspace closure condition conservative matrix conull conull matrix convergent columns coregular matrix coregular triangle Corollary defined DEFINITION dense divergent sequence dual equipotent equivalent exists finite FK program FK space Frechet space functional analysis given growth sequence Hahn-Banach theorem Hausdorff hence implies includes inset integers invariant kth column Lemma Let Ax)n Let f limAx locally convex locally convex space matrix with convergent Mercerian monotone norm multiplicative Necessity notation of Remark null columns proof proved regular relative topology replaceable result follows row function row-finite seminorms shows Sufficiency summability suppose t(Ax tA)x Tauberian Theorem 12 Theorem 9 trivial u-continuous u-unique vector space weakly