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Displaying similar documents to “RUC systems in rearrangement invariant spaces”

Sequences of independent identically distributed functions in rearrangement invariant spaces

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.

On a secondary invariant of the hyperelliptic mapping class group

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.

On invariant subspaces for polynomially bounded operators

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...

Invariant Means on Banach Spaces

Radosław Łukasik (2017)

Annales Mathematicae Silesianae

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In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.

Existence and construction of two-dimensional invariant subspaces for pairs of rotations

Ernst Dieterich (2009)

Colloquium Mathematicae

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By a rotation in a Euclidean space V of even dimension we mean an orthogonal linear operator on V which is an orthogonal direct sum of rotations in 2-dimensional linear subspaces of V by a common angle α ∈ [0,π]. We present a criterion for the existence of a 2-dimensional subspace of V which is invariant under a given pair of rotations, in terms of the vanishing of a determinant associated with that pair. This criterion is constructive, whenever it is satisfied. It is also used to prove...

AK-invariant, some conjectures, examples and counterexamples

L. Makar-Limanov (2001)

Annales Polonici Mathematici

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In my talk I am going to remind you what is the AK-invariant and give examples of its usefulness. I shall also discuss basic conjectures about this invariant and some positive and negative results related to these conjectures.