On the joint spectral radius of a nilpotent Lie algebra of matrices

Enrico Boasso

Displaying similar documents to “On the joint spectral radius of a nilpotent Lie algebra of matrices”

On the joint spectral radius of commuting matrices

Rajendra Bhatia, Tirthankar Вhattacharyya (1995)

Studia Mathematica

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For a commuting n-tuple of matrices we introduce the notion of a joint spectral radius with respect to the p-norm and prove a spectral radius formula.

Spectral radius preservers of products of monnegative matrices.

Clark, Sean, Li, Chi-Kwong, Rodman, Leiba (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Inequalities for exponentials in Banach algebras

A. Pryde (1991)

Studia Mathematica

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For commuting elements x, y of a unital Banach algebra ℬ it is clear that $∥ e^{x + y} ∥ \leq ∥ e^{x} ∥ ∥ e^{y} ∥$ . On the order hand, M. Taylor has shown that this inequality remains valid for a self-adjoint operator x and a skew-adjoint operator y, without the assumption that they commute. In this paper we obtain similar inequalities under conditions that lie between these extremes. The inequalities are used to deduce growth estimates of the form $∥ e^{'} ∥ \leq c (1 + | ξ | ⟩^{s}$ for all $ξ \in R^{m}$ , where $x = (x_{1}, . . ., x_{m}) \in ℬ^{m}$ and c, s are constants.

Comparison of joint spectra for certain classes of commuting operators

Alan McIntosh, Alan Pryde, Werner Ricker (1988)

Studia Mathematica

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Some classes of commuting n-tuples of operators

Muneo Chō, Makoto Takaguchi (1984)

Studia Mathematica

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Invariant subspaces and spectral mapping theorems

V. Shul'man (1994)

Banach Center Publications

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We discuss some results and problems connected with estimation of spectra of operators (or elements of general Banach algebras) which are expressed as polynomials in several operators, noncommuting but satisfying weaker conditions of commutativity type (for example, generating a nilpotent Lie algebra). These results have applications in the theory of invariant subspaces; in fact, such applications were the motivation for consideration of spectral problems. More or less detailed proofs...

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.