Conjugation-invariant means
V. Losert, H. Rindler (1987)
Colloquium Mathematicae
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V. Losert, H. Rindler (1987)
Colloquium Mathematicae
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Walter Rudin (1972)
Studia Mathematica
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D. R. Georgijević (1987)
Matematički Vesnik
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Aharon Atzmon (2001)
Annales de l’institut Fourier
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A criterion for reducibility of certain representations of abelian groups is established. Among the applications of this criterion, we give a positive answer to the translation invariant subspace problem for weighted spaces on locally compact abelian groups, for even weights and .
Edvard Kramar (1997)
Commentationes Mathematicae Universitatis Carolinae
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The invariant subspace problem for some operators and some operator algebras acting on a locally convex space is studied.
T. Husain, James C. S. Wong (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Kushpel', N.N. (2005)
Journal of Mathematical Sciences (New York)
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Junfeng Liu (2017)
Czechoslovak Mathematical Journal
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We discuss the invariant subspace problem of polynomially bounded operators on a Banach space and obtain an invariant subspace theorem for polynomially bounded operators. At the same time, we state two open problems, which are relative propositions of this invariant subspace theorem. By means of the two relative propositions (if they are true), together with the result of this paper and the result of C. Ambrozie and V. Müller (2004) one can obtain an important conclusion that every polynomially...
Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2009)
Open Mathematics
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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. ...