\(\gamma \)-bounded representations of amenable groups

DOI10.1016/j.aim.2010.01.019zbMath1209.22004arXiv1003.1587OpenAlexW2068558332MaRDI QIDQ977510

Christian Le Merdy

Publication date: 22 June 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.1587

zbMATH Keywords

amenabilitybounded representations\(\gamma\)-boundedness

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Functional calculus for linear operators (47A60) Probabilistic methods in Banach space theory (46B09) Other representations of locally compact groups (22D12)

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Isometric dilations and 𝐻^{∞} calculus for bounded analytic semigroups and Ritt operators ⋮ Euclidean Structures and Operator Theory in Banach Spaces ⋮ Functional calculus for a bounded \(C_0\)-semigroup on Hilbert space ⋮ Functional calculus and dilation for \(C_{0}\)-groups of polynomial growth ⋮ Transference principles for semigroups and a theorem of Peller ⋮ A Besov algebra calculus for generators of operator semigroups and related norm-estimates ⋮ $\gamma $-boundedness of $C_0$-semigroups and their $H^{\infty }$-functional calculi ⋮ New properties of the multivariable \(H^\infty\) functional calculus of sectorial operators ⋮ Derivative bounded functional calculus of power bounded operators on Banach spaces ⋮ NEW COUNTEREXAMPLES ON RITT OPERATORS, SECTORIAL OPERATORS AND -BOUNDEDNESS

Cites Work

• The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
• Solution of the similarity problem for cyclic representations of \(C^*- algebras\)
• Stochastic evolution equations in UMD Banach spaces
• Singular convolution integrals with operator-valued kernel
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Stochastic integration in UMD Banach spaces
• \(R\)-bounded representations of \(L^1(G)\)
• Admissibility of unbounded operators and well-posedness of linear systems in Banach spaces
• On operator-valued Fourier multiplier theorems
• A T1 theorem for integral transformations with operator-valued kernel
• TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY
• Abstract Spectral Decompositions Guaranteed by the Hilbert Transform
• The Similarity Problem for Representations of C ∗ -Algebras
• On Non Self-Adjoint Representations of C*-Algebras
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Fourier embeddings and Mihlin‐type multiplier theorems
• Weighted Admissibility and Wellposedness of Linear Systems in Banach Spaces
• C (K) -representations and R -boundedness
• H^p-Maximal Regularity and Operator Valued Multipliers on Hardy Spaces
• Wavelet transform for functions with values in UMD spaces
• The main triangle projection in matrix spaces and its applications
• Similarity problems and completely bounded maps. Includes the solution to ``The Halmos problem.
• A strong similarity property of nuclear \(C^*\)-algebras
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity
• The \(H^\infty\)-calculus and sums of closed operators
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