scholarly journals Invariant means on Abelian groups capture complementability of Banach spaces in their second duals

2021 ◽  
Author(s):  
Adam P. Goucher ◽  
Tomasz Kania
Keyword(s):  
Banach Spaces ◽  
Abelian Groups ◽  
Invariant Means

scholarly journals Invariant Means on Banach Spaces

2017 ◽  
Vol 31 (1) ◽  
pp. 127-140
Author(s):  
Radosław Łukasik
Keyword(s):  
Banach Spaces ◽  
Invariant Mean ◽  
Sufficient Condition ◽  
Invariant Means

Abstract In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.

scholarly journals RIEMANNLEBESGUE PROPERTIES OF BANACH SPACES ASSOCIATED WITH SUBSETS OF COUNTABLE DISCRETE ABELIAN GROUPS

2003 ◽  
Vol 45 (1) ◽  
pp. 159-166
Author(s):  
PATRICK N. DOWLING ◽  
NARCISSE RANDRIANANTOANINA
Keyword(s):  
Banach Spaces ◽  
Abelian Groups

The Range of Invariant Means on Locally Compact Abelian Groups

1974 ◽  
Vol 17 (4) ◽  
pp. 567-573
Author(s):  
Roy C. Snell
Keyword(s):  
Abelian Groups ◽  
Invariant Mean ◽  
Discrete Groups ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
Invariant Means

AbstractIt has been shown by E. Granirer that for certain infinite amenable discrete groups G there exists a nested family of left almost convergent subsets of G on which every left invariant mean on m(G) attains as its range the entire [0,1] interval. This paper examines the range of left invariant means on L∞(G) for infinite locally compact abelian groups G and demonstrates the existence in every such group of a nested family of left almost convergent Borel subsets on which every left invariant mean on L∞ (G) attains as its range the interval [0,1],

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