The homotopy type of the linear group of the Banach space

1980 ◽  
pp. 169-174
Author(s):  
L. S. Belov
Keyword(s):  
Banach Space ◽  
Linear Group ◽  
Homotopy Type

On the contractibility to a point of the linear groups of reflexive non-commutative Lp-spaces

1996 ◽  
Vol 119 (3) ◽  
pp. 545-560 ◽  
Author(s):  
Sergei V. Ferleger ◽  
Fyodor A. Sukochev
Keyword(s):  
Banach Space ◽  
Linear Group ◽  
Operator Norm ◽  
Linear Groups ◽  
Lp Spaces ◽  
Continuous Map

For every Banach space X, denote by GL(X) the linear group of X, i.e. the group of all linear continuous invertible operators on X with the topology induced by the operator norm. One says that GL(X) is contractible to a point if there exists a continuous map F: GL(X) × [0, 1] → GL(X) such that F(A,0) = A and F(A, 1) = Id, for every A ∈ GL(X).

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

The smooth case

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Homotopy Type ◽  
Unit Vector ◽  
Smooth Case ◽  
Open Set ◽  
Birational Invariant

This chapter examines the simplifications occurring in the proof of the main theorem in the smooth case. It begins by stating the theorem about the existence of an F-definable homotopy h : I × unit vector X → unit vector X and the properties for h. It then presents the proof, which depends on two lemmas. The first recaps the proof of Theorem 11.1.1, but on a Zariski dense open set V₀ only. The second uses smoothness to enable a stronger form of inflation, serving to move into V₀. The chapter also considers the birational character of the definable homotopy type in Remark 12.2.4 concerning a birational invariant.

Sign in / Sign up

Export Citation Format

Share Document