Strict, weighted, and mixed topologies and applications

DOI10.1016/0001-8708(76)90062-1zbMath0347.46023OpenAlexW2087616117MaRDI QIDQ1234042

Heron S. Collins

Publication date: 1976

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(76)90062-1

Mathematics Subject Classification ID

Real- or complex-valued set functions (28A10) General theory of (C^*)-algebras (46L05) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Topological linear spaces of continuous, differentiable or analytic functions (46E10) General theory of locally convex spaces (46A03) Duality theory for topological vector spaces (46A20) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Rings and algebras of continuous, differentiable or analytic functions (46E25) Miscellaneous applications of functional analysis (46N99) Ideals and subalgebras (46H10)

Related Items

THE STRICT TOPOLOGY ON THE DISCRETE LEBESGUE SPACES ⋮ Mackey topologies and mixed topologies in Riesz spaces ⋮ Approximate Identities and Paracompactness ⋮ Certain strict topologies on the space of regular Borel measures on locally compact groups ⋮ The extension and completion of the universal measure and the dual of the space of measures ⋮ Closed graph theorems for generalized inductive limit topologies ⋮ On the locally convex structure of strict topologies ⋮ Locally convex infinitesimal calculus. 2. Computations on Mackey \((\ell^{\infty})\) ⋮ The finest Nachbin topology is a mixed topology

Cites Work

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• Bounded continuous functions on a locally compact space
• A generalization of the Stone-Weierstrass theorem
• Kernels of measures on completely regular spaces
• Linear functionals and partitions of unity in C\(_b\)(X)
• Weighted approximation for algebras and modules of continuous functions. Real and self-adjoint complex cases
• On the spectral analysis of bounded functions
• The space of bounded analytic functions on a region
• Remarks on certain function spaces
• Bounded continuous vector-valued functions on a locally compact space
• On the space \(1^ \infty (S)\), with the strict topology
• Interpolation in \(W^ *\)-algebras
• Compact and weakly compact operators on \(C(S)_\beta\)
• Compactness and convergence in the space of measures
• The bounded weak-star topology and the bounded analytic functions
• A theorem on sequential convergence of measures and some applications
• Bishop's generalized Stone-Weierstraß theorem for weighted spaces
• The general complex bounded case of the strict weighted approximation problem
• The strict topology on bounded sets
• Le convexe topologique des probabilités sur un espace topologique. (The topological convexity of probabilities on a topological space)
• The bounded weak star topology and the general strict topology
• Weighted approximation, vector fibrations and algebras of operators
• A general Phillips theorem for \(C^*\)-algebras an d some applications
• The strict topology, separable measures, and paracompactness
• Interpolation in algebras of operator fields
• Lokalkonvexe Unterräume in topologischen Vektorräumen und das \(\varepsilon\)-Produkt
• Approximate identities and the strict topology
• Un théorème sur les fonctions bornees et uniformement continues sur l'axe réel
• On spectral analysis in the narrow topology
• The Spectral Theory of Bounded Functions
• Linear spaces with mixed topology
• On Compactness in Spaces of Measures and Measurecompact Spaces
• Topological Measure Theory for Double Centralizer Algebras
• The Strict Topology for P-Spaces
• The strict topology and compactness in the space of measures
• Subspaces of 𝐶(𝑆)ᵦ, the space (𝑙^{∞},𝛽), and (𝐻^{∞},𝛽)
• Stone-Weierstrass Theorems for the Strict Topology
• An Introduction to the Theory of Centralizers
• On Baire measures on D-topological spaces
• Convergence of Baire measures
• Measures on Topological Spaces
• The Additivity of Measures on Completely Regular Spaces
• A Generalized Form of Inductive-Limit Topology for Vector Spaces
• Double Centralizers and Extensions of C ∗ -Algebras
• The Strict Topology and Compactness in the space of Measures. II
• Some Applications of Hewitt's Factorization Theorem
• The Localization of the Strict Topology Via Bounded Sets
• Factorization in Banach Algebras and the General Strict Topology
• Measures and Mappings on Topological Spaces
• A Representation Theorem for Biequicontinuous Completed Tensor Products of Weighted Spaces
• The second duals of certain spaces of analytic functions
• Measures on Metacompact Spaces
• Dual Spaces of Weighted Spaces
• The Strict Topology for Double Centralizer Algebras
• A Generalization of the Strict Topology
• Bounded convergence of analytic functions
• Factorization in Fréchet spaces
• Conditions for equality of the Mackey and strict topologies
• Weak Topologies on Subspaces of C(S)
• The Strict Topology in a Completely Regular Setting: Relations to Topological Measure Theory
• The Strict Topology and Spaces with Mixed Topologies
• Weighted approximation for modules of continuous functions
• Bounded Measures on Topological Spaces
• Bounded Continuous Functions on a Completely Regular Space
• Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I.
• The $\sigma$-Compact-Open Topology and its Relatives.
• Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. II.
• Metric spaces in which Prohorov's theorem is not valid
• A Generalization of the Strict Topology.
• Separability in the Strict and Substrict Topologies
• Double centralizers of Pedersen's ideal of a $C^* $-algebra
• Noncoincidence of the Strict and Strong Operator Topologies
• Strict Topologies for Vector-Valued Functions
• Double centralizers of Pedersen’s ideal of a 𝐶*-algebra. II
• Bishop's Generalized Stone-Weierstrass Theorem for the Strict Topology
• Centralisers on Certain Topological Algebras
• On approximation by polynomials to a function analytic in a simply connected region
• Operator Algebras and Dual Spaces
• Completeness and Compactness in Linear Topological Spaces