Search results for "Closed graph theorem"

showing 6 items of 6 documents

A theorem of insertion and extension of functions for normal spaces

1993

Discrete mathematicsPure mathematicsArzelà–Ascoli theoremIsomorphism extension theoremFréchet spaceGeneral MathematicsClosed graph theoremRiesz–Thorin theoremOpen mapping theorem (functional analysis)Brouwer fixed-point theoremMathematicsCarlson's theoremArchiv der Mathematik
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The Bishop–Phelps–Bollobás theorem for operators

2008

AbstractWe prove the Bishop–Phelps–Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop–Phelps–Bollobás theorem holds for operators from ℓ1 into Y. Several examples of classes of such spaces are provided. For instance, the Bishop–Phelps–Bollobás theorem holds when the range space is finite-dimensional, an L1(μ)-space for a σ-finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.

Discrete mathematicsPure mathematicsMathematics::Functional AnalysisApproximation propertyEberlein–Šmulian theoremBanach spaceNorm attainingBishop–Phelps theoremUniform boundedness principleUniform convexityInterpolation spaceOperatorClosed graph theoremReflexive spaceBishop–Phelps theoremAnalysisMathematicsJournal of Functional Analysis
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A note on the closed graph theorem

1977

Discrete mathematicsUniform boundedness principleDual spaceGeneral MathematicsBanach spaceClosed graph theoremLp spaceReflexive spaceQuotient space (linear algebra)Complete metric spaceMathematicsArchiv der Mathematik
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Counterexamples to the Algebraic Closed Graph Theorem

1982

Discrete mathematicssymbols.namesakeAlgebraic graph theoryGeneral MathematicsPerfect graphsymbolsGraph minorPerfect graph theoremClosed graph theoremRobertson–Seymour theoremPlanar graphMathematicsExtremal graph theoryJournal of the London Mathematical Society
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Selected Topics on Banach Space Theory

2019

Basic topics on Banach space theory needed for the text are reviewed. Hahn-Banach theorem, Baire’s theorem, uniform boundedness principle, closed graph theorem, weak topologies, Banach-Alaoglu theorem, unconditional basis, Banach sequence spaces, summing operators, factorable operators, cotype, Kahane inequality.

Mathematics::Functional AnalysisPure mathematicsSequenceBasis (linear algebra)Uniform boundedness principleBanach spaceMathematics::General TopologyHahn–Banach theoremClosed graph theoremMathematicsSchauder basis
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On Słowikowski, Raíkov and De Wilde Closed Graph Theorems

1986

Publisher Summary This chapter focuses on the Slowikowski, Raikov and De Wilde closed graph theorems. The vector spaces used in the chapter, are defined over the field Ղ of real or complex numbers. The term, “space” means separated topological vector space, unless the contrary is specifically stated. If Ω is a non-empty open subset of the n -dimensional euclidean space, then the Schwartz space ҟ′(Ω) endowed with the strong topology belongs to this class. The chapter also studies the classes of spaces related with this conjecture. The class of Slowikowski spaces contains the F-spaces and it is stable with respect to the operations that include: countable topological direct sums, closed subsp…

Topological manifoldDiscrete mathematicsPure mathematicsConnected spaceClosed setDense setLocally convex topological vector spaceClosed graph theoremTopological spaceTopological vector spaceMathematics
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