Matrix methods in analysis

DOI10.1007/BFB0072264zbMath0564.46001MaRDI QIDQ1058103

Piotr Antosik, Charles W. Swartz

Publication date: 1985

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

summabilityvector measuresbilinear mapsuniform boundedness principlesimbedding \(c_ 0\) and \(\ell ^{\infty }\) into Banach spacesK convergencenormed abelian group

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Matrix methods for summability (40C05) Classical Banach spaces in the general theory (46B25) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Vector-valued measures and integration (46G10) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19)

Related Items (39)

Remarks on regular \((LF)\)-spaces ⋮ The Hahn-Schur Theorem on effect algebras ⋮ Unnamed Item ⋮ On the barrelledness of spaces of bounded vector functions ⋮ Unnamed Item ⋮ Numerical approximations of singular source terms in differential equations ⋮ Subseries convergence in abstract duality pairs ⋮ On Antosik’s Lemma and the Antosik-Mikusinski Basic Matrix Theorem ⋮ Noncommutative version of Nikodym boundedness theorem for uniform space- valued functions ⋮ Weak sequential completeness of \(\beta\)-duals ⋮ An ideal topology type convergent theorem on scale effect algebras ⋮ Limit theorems in \((l)\)-groups with respect to \((D)\)-convergence ⋮ The Nikodým boundedness theorem for lattice-valued measures ⋮ Completely continuous and related multilinear operators ⋮ Unnamed Item ⋮ A remark about the statistical Cesàro summability and the Orlicz-Pettis theorem ⋮ The order topology on the projection lattice of a Hilbert space ⋮ Unnamed Item ⋮ The Schur lemma for bounded multiplier convergent series ⋮ On convergence of double series ⋮ The Vitali-Hahn-Saks Theorem and Measuroids ⋮ A summation theorem and its applications ⋮ Uniform convergence in topological groups ⋮ General Orlicz--Pettis theorem ⋮ Summing Boolean algebras ⋮ Unnamed Item ⋮ Subseries Convergence in Spaces with a Schauder Basis ⋮ A remark about the Orlicz-Pettis theorem and the statistical convergence ⋮ Equivalence of the Mikusiński–Shiraishi–Itano products in 𝒮′ for various classes of delta-sequences ⋮ Some new classes of Banach-Mackey spaces ⋮ Matrix summability methods and weakly unconditionally Cauchy series ⋮ The closed graph theorem without category ⋮ A Riemann type theorem for series of operators on Banach spaces ⋮ A generalisation of Mackey's theorem and the uniform boundedness principle ⋮ Weak property \((Y_0)\) and regularity of inductive limits ⋮ A unified convergence theorem ⋮ The gliding hump property in vector sequence spaces ⋮ Normed barrelled spaces ⋮ On the Mikusiński-Antosik diagonal theorem and the equivalence of two types of convergence in Köthe spaces

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