Displaying similar documents to “Vector-valued invariant means on spaces of bounded linear maps”

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.

RUC systems in rearrangement invariant spaces

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.

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 sets and Knaster-Tarski principle

Krzysztof Leśniak (2012)

Open Mathematics

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Our aim is to point out the applicability of the Knaster-Tarski fixed point principle to the problem of existence of invariant sets in discrete-time (multivalued) semi-dynamical systems, especially iterated function systems.

L¹ factorizations, moment problems and invariant subspaces

Isabelle Chalendar, Jonathan R. Partington, Rachael C. Smith (2005)

Studia Mathematica

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For an absolutely continuous contraction T on a Hilbert space 𝓗, it is shown that the factorization of various classes of L¹ functions f by vectors x and y in 𝓗, in the sense that ⟨Tⁿx,y⟩ = f̂(-n) for n ≥ 0, implies the existence of invariant subspaces for T, or in some cases for rational functions of T. One of the main tools employed is the operator-valued Poisson kernel. Finally, a link is established between L¹ factorizations and the moment sequences studied in the Atzmon-Godefroy...