Some Results from the General Theory of Banach Spaces

A theory of contractions of Lie algebra representations on complex Hilbert spaces is proposed, based on Trotter's theory of approximating sequences of Banach spaces. Its main distinguishing feature is a careful definition of the carrier space of the limit Lie algebra representation. A set of quite general conditions on the contracting representations, satisfied in all known examples, is proven to be sufficient for the existence of such a representation. In order to show how natural the suggested framework is, the general theory is applied to the contraction of [Formula: see text] into the Lie algebra [Formula: see text] of the 3-dimensional Heisenberg group and to the related study of the limit N→∞ of a quantum system of N identical two-level particles.

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Perturbed Optimization in Banach Spaces I: A General Theory Based on a Weak Directional Constraint Qualification

SIAM Journal on Control and Optimization ◽

10.1137/s0363012994267273 ◽

1996 ◽

Vol 34 (4) ◽

pp. 1151-1171 ◽

Cited By ~ 16

Author(s):

J. Frédéric Bonnans ◽

Roberto Cominetti

Keyword(s):

General Theory ◽

Banach Spaces ◽

Constraint Qualification ◽

Optimization In Banach Spaces ◽

Perturbed Optimization ◽

Directional Constraint

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Théorie générale d’équation de type hyperbolique-parabolique non linéaire

Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées ◽

10.46298/arima.1906 ◽

2008 ◽

Vol Volume 9, 2007 Conference in... ◽

Author(s):

Hamidou Touré

Keyword(s):

Weak Solution ◽

Group Theory ◽

General Theory ◽

Banach Spaces ◽

Mild Solution ◽

Existence Of Solutions ◽

Parabolic Type ◽

Semi Group ◽

Nous Montrons ◽

International Audience

International audience We develop general theory for degenerate hyperbolic-parabolic type problems using semi-group theory in Banach spaces. We establish existence, uniqness results and continuous dependance with respects to data for mild solution. Similar results are developped for weak solution of entropy type, and existence of solutions are studied. Nous développons une théorie générale pour des équations d’évolution de type hyperbolique parabolique non linéaire à l’aide de la théorie des semi-groupes non linéaires dans les espaces de Banach. Nous établissons des résultats d’existence, d’unicité et de dépendance continue par rapport aux données d’une bonne solution du problème de Cauchy ou des problèmes aux limites associées à cette équation sous des hypothèses très générales. Avec des hypothèses complémentaires, nous montrons que cette bonne solution est une solution locale de type entropique, nous étudions également l’unicité des solutions faibles et l’existence de solution forte.

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Inductive and projective limits of smooth topological vector spaces

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700044452 ◽

1972 ◽

Vol 6 (2) ◽

pp. 227-240 ◽

Cited By ~ 2

Author(s):

John W. Lloyd ◽

S. Yamamuro

Keyword(s):

General Theory ◽

Banach Spaces ◽

Vector Spaces ◽

Topological Vector Spaces ◽

Inductive And Projective Limits ◽

Nuclear Spaces ◽

Projective Limits ◽

The Relationship

In J. Math. Mech. 15 (1966), 877–898, Bonic and Frampton have laid the foundation for a general theory of smoothness of Banach spaces. In this paper, we shall study one aspect of the smoothness of topological vector spaces, namely, the relationship between smoothness and inductive and protective limits of topological vector spaces. As a consequence, we obtain smoothness results for nuclear spaces and some Montei spaces.

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Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

Behavioral and Brain Sciences ◽

10.1017/s0140525x18001620 ◽

2018 ◽

Vol 41 ◽

Cited By ~ 2

Author(s):

Daniel Crimston ◽

Matthew J. Hornsey

Keyword(s):

General Theory ◽

Biological Markers ◽

Natural Environment ◽

Relevant Dimension ◽

Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

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