Duality theorem for L-R crossed coproducts

We prove that sup(f-h)(E) = sup(h*-f*)(E*), where f is a proper lower semi-continuous convex functional on a real locally convex space E, h: E → = [-∞, +∞] is an arbitrary-functional and, f*, h* are their convex conjugates respectively. When h = δG, the indicator of a bounded subset G of E, this yields a formula for sup f(G).

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Takesaki–Takai Duality Theorem in Hilbert C*-Modules

Acta Mathematica Sinica English Series ◽

10.1007/s10114-004-0405-4 ◽

2004 ◽

Vol 20 (6) ◽

pp. 1079-1088

Author(s):

Mao Zheng Guo ◽

Xiao Xia Zhang

Keyword(s):

Duality Theorem

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A duality theorem for planar three-body Ising models and their vertex model equivalences

Journal of Physics A General Physics ◽

10.1088/0305-4470/10/2/012 ◽

1977 ◽

Vol 10 (2) ◽

pp. 229-238 ◽

Cited By ~ 7

Author(s):

D W Wood ◽

N E Pegg

Keyword(s):

Duality Theorem ◽

Ising Models ◽

Vertex Model ◽

Three Body

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On Grothendieck's local duality theorem

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100055870 ◽

1979 ◽

Vol 85 (3) ◽

pp. 431-437 ◽

Cited By ~ 3

Author(s):

M. H. Bijan-Zadeh ◽

R. Y. Sharp

Keyword(s):

Algebraic Geometry ◽

Commutative Algebra ◽

Noetherian Ring ◽

Duality Theorem ◽

Great Emphasis ◽

Triangulated Category ◽

Elementary Approach ◽

Commutative Noetherian Ring ◽

Local Duality ◽

Dualizing Complexes

In (11) and (12), a comparatively elementary approach to the use of dualizing complexes in commutative algebra has been developed. Dualizing complexes were introduced by Grothendieck and Hartshorne in (2) for use in algebraic geometry; the approach to dualizing complexes in (11) and (12) differs from that of Grothendieck and Hartshorne in that it avoids use of the concepts of triangulated category, derived category, and localization of categories, and instead places great emphasis on the concept of quasi-isomorphism of complexes of modules over a commutative Noetherian ring.

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Two Short Proofs Concerning Tree-Decompositions

Combinatorics Probability Computing ◽

10.1017/s0963548302005369 ◽

2002 ◽

Vol 11 (6) ◽

pp. 541-547 ◽

Cited By ~ 22

Author(s):

PATRICK BELLENBAUM ◽

REINHARD DIESTEL

Keyword(s):

Duality Theorem ◽

Finite Graph ◽

Tree Decomposition ◽

Tree Width ◽

Tree Decompositions

We give short proofs of the following two results: Thomas's theorem that every finite graph has a linked tree-decomposition of width no greater than its tree-width; and the ‘tree-width duality theorem’ of Seymour and Thomas, that the tree-width of a finite graph is exactly one less than the largest order of its brambles.

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