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1
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On some infinite dimensional linear groups

100%
Kurdachenko L., Sadovnichenko A., Subbotin I.
Open Mathematics
|
2009
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tom 7
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nr 2
176-185
EN
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
2
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Infinite dimensional linear groups with many G - invariant subspaces

100%
Kurdachenko L., Sadovnichenko A., Subbotin I.
Open Mathematics
|
2010
|
tom 8
|
nr 2
261-265
EN
Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.
3
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An introduction to Rota’s universal operators: properties, old and new examples and future issues

100%
Cowen C. C., Gallardo-Gutiérrez E. A.
Concrete Operators
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2016
|
tom 3
|
nr 1
43-51
EN
The Invariant Subspace Problem for Hilbert spaces is a long-standing question and the use of universal operators in the sense of Rota has been an important tool for studying such important problem. In this survey, we focus on Rota’s universal operators, pointing out their main properties and exhibiting some old and recent examples.
4
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An overview of some recent developments on the Invariant Subspace Problem

75%
Chalendar I., Partington J. R.
Concrete Operators
|
2013
|
tom 1
1-10
EN
This paper presents an account of some recent approaches to the Invariant Subspace Problem. It contains a brief historical account of the problem, and some more detailed discussions of specific topics, namely, universal operators, the Bishop operators, and Read’s Banach space counter-example involving a finitely strictly singular operator.
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