### On translation invariant families of sets

John C. Morgan II (1975)

Colloquium Mathematicae

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John C. Morgan II (1975)

Colloquium Mathematicae

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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.

Marek Jarnicki, Peter Pflug

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D. R. Georgijević (1987)

Matematički Vesnik

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Kurzweil, J.

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Takayuki Morifuji (2009)

Banach Center Publications

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We discuss relations among several invariants of 3-manifolds including Meyer's function, the η-invariant, the von Neumann ρ-invariant and the Casson invariant from the viewpoint of the mapping class group of a surface.

Sebastian Goette (2014)

Journal of the European Mathematical Society

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As an application, we compute the Eells–Kuiper and t-invariants of certain cohomogeneity one manifolds that were studied by Dearricott, Grove, Verdiani, Wilking, and Ziller. In particular, we determine the diffeomorphism type of a new manifold of positive sectional curvature.

V. Losert, H. Rindler (1987)

Colloquium Mathematicae

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D.M. Jr. Burns, C.L. Epstein (1988)

Inventiones mathematicae

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Mircea Puta (1984)

Časopis pro pěstování matematiky

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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.

Hirică, Iulia Elena (1999)

Balkan Journal of Geometry and its Applications (BJGA)

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Jian-Qiang, Li, Zexuan, Zhu, Zhen, Ji, Hai-Long, Pei (2010)

Mathematical Problems in Engineering

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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...