Displaying similar documents to “On Lp Spectral Multipliers for a Solvable Lie Group.”

Quasispectra of solvable Lie algebra homomorphisms into Banach algebras

Anar Dosiev (2006)

Studia Mathematica

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We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism π of a finite-dimensional solvable Lie algebra 𝔤 in terms of quasispectra σ(π). In particular, we prove that the joint spectral radius of a compact subset in a solvable operator Lie subalgebra coincides with the geometric spectral radius with respect to a quasispectrum.

Analytic joint spectral radius in a solvable Lie algebra of operators

Daniel Beltiţă (2001)

Studia Mathematica

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We introduce the concept of analytic spectral radius for a family of operators indexed by some finite measure space. This spectral radius is compared with the algebraic and geometric spectral radii when the operators belong to some finite-dimensional solvable Lie algebra. We describe several situations when the three spectral radii coincide. These results extend well known facts concerning commuting n-tuples of operators.

Sub-Laplacians of holomorphic L p -type on exponential Lie groups

Detlef Müller (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this survey article, I shall give an overview on some recent developments concerning the L p -functional calculus for sub-Laplacians on exponential solvable Lie groups. In particular, I shall give an outline on some recent joint work with W. Hebisch and J. Ludwig on sub-Laplacians which are of holomorphic L p -type, in the sense that every L p -spectral multiplier for p ≠ 2 will be holomorphic in some domain.

Lie solvable groups algebras of derived length three.

Meena Sahai (1995)

Publicacions Matemàtiques

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Let K be a field of characteristic p > 2 and let G be a group. Necessary and sufficient conditions are obtained so that the group algebra KG is strongly Lie solvable of derived length at most 3. It is also shown that these conditions are equivalent to KG Lie solvable of derived length 3 in characteristic p ≥ 7.

Spectrum for a solvable Lie algebra of operators

Daniel Beltiţă (1999)

Studia Mathematica

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A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.