Absolute continuity for Banach space valued mappings

2007 ◽  
Vol 56 (1) ◽  
pp. 116-124
Author(s):  
Cristina Di Bari ◽  
Calogero Vetro
Keyword(s):  
Banach Space ◽  
Absolute Continuity

scholarly journals Anosov diffeomorphisms, anisotropic BV spaces and regularity of foliations

2021 ◽  
pp. 1-37
Author(s):  
WAEL BAHSOUN ◽  
CARLANGELO LIVERANI
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Absolute Continuity ◽  
Hyperbolic Systems ◽  
Transfer Operator ◽  
Statistical Properties ◽  
Functions Of Bounded Variation ◽  
Expanding Maps ◽  
New Information ◽  
Piecewise Expanding Maps

Abstract Given any smooth Anosov map, we construct a Banach space on which the associated transfer operator is quasi-compact. The peculiarity of such a space is that, in the case of expanding maps, it reduces exactly to the usual space of functions of bounded variation which has proved to be particularly successful in studying the statistical properties of piecewise expanding maps. Our approach is based on a new method of studying the absolute continuity of foliations, which provides new information that could prove useful in treating hyperbolic systems with singularities.

DECOMPOSITIONS OF SPACES OF MEASURES

2008 ◽  
Vol 11 (01) ◽  
pp. 119-126
Author(s):  
IOANNIS ANTONIOU ◽  
COSTAS KARANIKAS ◽  
STANISLAV SHKARIN
Keyword(s):  
Banach Space ◽  
Absolute Continuity ◽  
Linear Subspace ◽  
Decomposition Theorem ◽  
Measurable Space ◽  
Jordan Decomposition ◽  
Closed Linear Subspace ◽  
Complex Valued ◽  
Spaces Of Measures ◽  
Nikodym Theorem

Let 𝔐 be the Banach space of σ-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of 𝔐 is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon–Nikodým theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen–Wintner purity theorem for our decompositions.

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
Sign in / Sign up

Export Citation Format

Share Document