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Matrix Transformations and Invariant Mean

Journal of King Abdulaziz University-Science, 2012
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On Invariant Means which are Not Inverse Invariant

Canadian Journal of Mathematics, 1968
In (1) R. G. Douglas says: “For a finite abelian group there exists a unique invariant mean which must be inversion invariant. For an infinite torsion abelian group it is not clear what the situation is.” It is not hard to see that if every element of an abelian group G is of order 2, then every invariant mean on G is also inversion invariant (see 1 ...
Rajagopalan, M., Witz, K. G.
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Topological inner invariant means

Studia Scientiarum Mathematicarum Hungarica, 2003
For a locally compact group G, we investigate topological inner invariant means on L8(G) and its subspaces. In particular, we characterize strict inner amenability of L1(G) to study the relation between this notion and strict inner amenability of G.
Memarbashi, R., Riazi, A.
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Repetition invariant geometric means

Linear Algebra and its Applications, 2018
Let \(\P:=\P_m\) be the space of all \(m\times m\) positive definite matrices. On the one hand, it is a convex cone of \(\mathbb H:=\mathbb H_m\), the Euclidean space of \(m\times m\) Hermitian matrices. On the other hand, it is a Riemannian-Cartan manifold and a simply connected complete Riemannian manifold with non-positive sectional curvature, if we
Sejong Kim, Hosoo Lee, Yongdo Lim
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Invariant Means.

1967
Doctor of Education (EdD) ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/185099/2/6807650 ...
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Invariance, Symmetry and Meaning

Foundations of Physics, 2000
The role of the concept of invariance in physics and geometry is analyzed, with attention to the closely connected concepts of symmetry and objective meaning. The question of why the fundamental equations of physical theories are not invariant, but only covariant, is examined in some detail.
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Invariant means on CHART groups

2015
Summary: The purpose of this paper is to give a stream-lined proof of the existence and uniqueness of a right-invariant mean on a CHART group. A CHART group is a slight generalisation of a compact topological group. The existence of an invariant mean on a CHART group can be used to prove Furstenberg's fixed point theorem.
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On the Set of Invariant Means

Journal of the London Mathematical Society, 1988
Adapting a technique used by \textit{C. Chou} [Trans. Am. Math. Soc. 273, 207-229 (1982; Zbl 0507.22007)] which consists in embedding a large set into the set of all invariant means, the author establishes the following theorem: If G is a locally compact noncompact amenable group, then the set of all topological invariant, inversion invariant means on \
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Invariant Means on Semigroups

2019
Let S be a semigroup, that is, a set endowed with an associative product $$(s, t)\mapsto st.$$ We consider the (real) Banach space of all real-valued bounded functions on S, namely, $$\ell ^\infty (S)=\Big \{f:S\rightarrow {\mathbb R}\,\,\,\text { such that}\,\,\,\Vert f\Vert \doteq \sup _{s\in S}|f(s)|
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