The lie algebra of a Banach space

1985 ◽  
pp. 129-157 ◽  
Author(s):  
Haskell Rosenthal
Keyword(s):  
Banach Space ◽  
Lie Algebra

The path functor and faithful representability of banach lie algebras

1973 ◽  
Vol 16 (1) ◽  
pp. 54-69 ◽  
Author(s):  
W. T. van Est ◽  
S. Świerczkowski
Keyword(s):  
Banach Space ◽  
Vector Space ◽  
Banach Algebra ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Uniform Norm

In this note “vector space” will mean “Banach space” unless otherwise specified. Accordingly “Lie algebra” will stand for “Banach Lie algebra”. Morphisms between Lie algebras will be assumed continuous. A Banach algebra B will be always assumed associative, and it will be also viewed as a Lie algebra with product [X, YXY− YX. In particular, the Lie algebra gl(V) of endomorphisms of a vector space V will be equipped with the uniform norm. A morphism of Lie algebras L → gl(V) will b called a representation of L in gl(V). Also, if B is a Banach algebra, a morphism of Lie algebras L → B will be called a representation of L in B. From such one evidently obtains a representation of L in gl(B). A representation will be called faithful if it is injective.

Infinite Dimensional DeWitt Supergroups and their Bodies

2014 ◽  
Vol 57 (2) ◽  
pp. 283-288 ◽  
Author(s):  
Ronald Fulp
Keyword(s):  
Banach Space ◽  
Lie Algebra ◽  
Lie Group ◽  
Grassmann Algebra ◽  
The Body ◽  
Exponential Mapping ◽  
Infinite Dimensional ◽  
Group Operation ◽  
Banach Lie Group ◽  
Quotient Manifold

AbstractFor Dewitt super groups G modeled via an underlying finitely generated Grassmann algebra it is well known that when there exists a body group BG compatible with the group operation on G, then, generically, the kernel K of the body homomorphism is nilpotent. This is not true when the underlying Grassmann algebra is infinitely generated. We show that it is quasi-nilpotent in the sense that as a Banach Lie group its Lie algebra κ has the property that for each a ∊ κ ada has a zero spectrum. We also show that the exponential mapping from κ to K is surjective and that K is a quotient manifold of the Banach space κ via a lattice in κ.

PROPRIÉTÉ (T) RENFORCÉE BANACHIQUE ET TRANSFORMATION DE FOURIER RAPIDE

2009 ◽  
Vol 01 (03) ◽  
pp. 191-206 ◽  
Author(s):  
VINCENT LAFFORGUE
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Simple Group ◽  
Banach Spaces ◽  
Lie Algebra ◽  
Local Field ◽  
Duke Math ◽  
Isometric Action ◽  
Property T

Let F be a non archimedean local field and let G be an algebraic connected almost F-simple group over F, whose Lie algebra contains sl3(F). We prove that G(F) has strong Banach property (T) in a stronger sense than in the article "Un renforcement de la propriété (T)", published in Duke Math. J. As a consequence, families of expanders built from a lattice in G(F) do not embed uniformly in Banach spaces of type > 1. Also any affine isometric action of G(F) on a Banach space of type > 1 has a fixed point.

ON FULLY CONVEX AND LOCALLY FULLY CONVEX BANACH SPACE

1990 ◽  
Vol 10 (3) ◽  
pp. 327-343 ◽  
Author(s):  
Qiyuan Na
Keyword(s):  
Banach Space ◽  
Convex Banach Space

Three Kinds of Numerical Indices of a Banach Space

2012 ◽  
Vol 112 (1) ◽  
pp. 21-35 ◽  
Author(s):  
Sung Guen Kim
Keyword(s):  
Banach Space
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