The Brezis-Browder theorem in a general Banach space

DOI10.1016/j.jfa.2012.03.023zbMath1259.47065arXiv1110.5706OpenAlexW2068813150WikidataQ56935494 ScholiaQ56935494MaRDI QIDQ428830

Heinz H. Bauschke, Liangjin Yao, Jonathan M. Borwein, Shawn Xianfu Wang

Publication date: 25 June 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5706

zbMATH Keywords

monotone operatoradjointsymmetric operatorset-valued operatorlinear relationBrezis-Browder theoremoperator of type (D)operator of type (FP)operator of type (NI)skew operator

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Set-valued operators (47H04) Duality theory (optimization) (49N15)

Related Items (8)

Epi-convergence: the Moreau envelope and generalized linear-quadratic functions ⋮ On non-enlargeable positive sets ⋮ Linear \(L\)-positive sets and their polar subspaces ⋮ Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator ⋮ Polar subspaces and automatic maximality ⋮ Rectangularity and paramonotonicity of maximally monotone operators ⋮ Equivalence betweenp-cyclic quasimonotonicity andp-cyclic monotonicity of affine maps ⋮ Remarks on p-cyclically monotone operators

Cites Work

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• A note on epsilon-subgradients and maximal monotonicity
• Fifty years of maximal monotonicity
• Convex functions, monotone operators and differentiability.
• Construction of pathological maximally monotone operators on non-reflexive Banach spaces
• Examples of discontinuous maximal monotone linear operators and the solution to a recent problem posed by B.F. Svaiter
• Minimax monotonicity
• Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators
• Monotone operators representable by l.s.c. convex functions
• Bounded approximants to monotone operators on Banach spaces
• The range of a monotone operator
• Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type
• Linear \(L\)-positive sets and their polar subspaces
• Set-valued mappings and enlargement of monotone operators.
• From Hahn--Banach to monotonicity
• Extension of Fenchel's duality theorem for convex functions
• On the continuity of biconjugate convex functions
• The Brézis-Browder Theorem Revisited and Properties of Fitzpatrick Functions of Order n
• On Gossez type (D) maximal monotone operators
• Banach SSD spaces and classes of monotone sets
• On Borwein–Wiersma Decompositions of Monotone Linear Relations
• Adjoint Process Duality
• Fitzpatrick Functions and Continuous Linear Monotone Operators
• Singular Hammerstein equations and maximal monotone operators
• On a Convexity Property of the Range of a Maximal Monotone Operator
• An Introduction to Banach Space Theory
• Maximality of sums of two maximal monotone operators in general Banach space
• On the Range of a Coercive Maximal Monotone Operator in a Nonreflexive Banach Space
• Monotone Linear Relations: Maximality and Fitzpatrick Functions
• Convex analysis and monotone operator theory in Hilbert spaces
• Five kinds of maximal monotonicity

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