P. G. Dodds, E. M. Semenov, F. A. Sukochev (2002)
Studia Mathematica
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We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.
John C. Morgan II (1975)
Colloquium Mathematicae
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D. R. Georgijević (1987)
Matematički Vesnik
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V. Losert, H. Rindler (1987)
Colloquium Mathematicae
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Colin C. Graham, Anthony To-Ming Lau, Michael Leinert (1988)
Colloquium Mathematicae
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Mircea Puta (1984)
Časopis pro pěstování matematiky
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Marek Jarnicki, Peter Pflug
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de la Llave, R. (2003)
Mathematical Physics Electronic Journal [electronic only]
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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...
G.A. Margulis, A.T. Huckleberry (1983)
Inventiones mathematicae
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Liu, Caiping, Yang, Xinmin (2009)
Journal of Inequalities and Applications [electronic only]
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S. V. Astashkin, F. A. Sukochev (2008)
Banach Center Publications
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A new set of sufficient conditions under which every sequence of independent identically distributed functions from a rearrangement invariant (r.i.) space on [0,1] spans there a Hilbertian subspace are given. We apply these results to resolve open problems of N. L. Carothers and S. L. Dilworth, and of M. Sh. Braverman, concerning such sequences in concrete r.i. spaces.