Displaying similar documents to “L¹ factorizations, moment problems and invariant subspaces”

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...

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.

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.

Vector-valued invariant means on spaces of bounded linear maps

Mahshid Dashti, Rasoul Nasr-Isfahani, Sima Soltani Renani (2013)

Colloquium Mathematicae

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Let 𝓐 be a Banach algebra and let ℳ be a W*-algebra. For a homomorphism Φ from 𝓐 into ℳ, we introduce and study ℳ -valued invariant Φ-means on the space of bounded linear maps from 𝓐 into ℳ. We establish several characterizations of existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ). We also study the relation between existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ) and amenability of 𝓐. Finally, for a character ϕ of 𝓐, we give some descriptions for ϕ-amenability of 𝓐 in...

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...

Invariant subspaces on multiply connected domains.

Ali Abkar, Hakan Hedenmalm (1998)

Publicacions Matemàtiques

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The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω­. The main result reads as follows: Assume that B is a Banach space of...