Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras

Enrico Boasso

Displaying similar documents to “Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras”

Tensor products and joint spectra for solvable Lie algebras of operators.

Enrico Boasso (1998)

Collectanea Mathematica

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Three spectral notions for representations of commutative Banach algebras

Yngve Domar, Lars-Ake Lindahl (1975)

Annales de l'institut Fourier

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Let $T$ be a bounded representation of a commutative Banach algebra $B$ . The following spectral sets are studied. $Λ_{1} (T)$ : the Gelfand space of the quotient algebra $B / Ker T$ . $Λ_{2} (T)$ : the Gelfand space of the operator algebra $Im T$ . $Λ_{3} (T)$ : those characters $φ$ of $B$ for which the inequalities $∥ T_{b} x - \hat{b} (φ) x ∥ < ϵ ∥ x ∥$ , $b \in F$ , have a common solution $x \neq 0$ , for any $ϵ > 0$ and any finite subset $F$ of $B$ . A theorem of Beurling on the spectrum of $L^{\infty}$ -functions and results of Slodkowski and Zelazko on joint topological divisors of zero appear as special cases of...

The norm spectrum in certain classes of commutative Banach algebras

H. S. Mustafayev (2011)

Colloquium Mathematicae

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Let A be a commutative Banach algebra and let $Σ_{A}$ be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by $σ (f) = \bar{f \cdot a : a \in A} \cap Σ_{A}$ , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.

Ascent spectrum and essential ascent spectrum

O. Bel Hadj Fredj, M. Burgos, M. Oudghiri (2008)

Studia Mathematica

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We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if $σ_{a s c}^{e} (T + F) = σ_{a s c}^{e} (T)$ for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued...

Conditions equivalent to C* independence

Shuilin Jin, Li Xu, Qinghua Jiang, Li Li (2012)

Studia Mathematica

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Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , $S p (A, B) = S p (A) \times S p (B)$ , where Sp denotes the joint Taylor spectrum.

On certain products of Banach algebras with applications to harmonic analysis

Mehdi Sangani Monfared (2007)

Studia Mathematica

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Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product $A \times_{θ} B$ , which is a strongly splitting Banach algebra extension of B by A. We obtain characterizations of bounded approximate identities, spectrum, topological center, minimal idempotents, and study the ideal structure of these products. By assuming B to be a Banach algebra in ₀(X) whose spectrum can be identified with X, we apply our results to harmonic analysis, and study the question of spectral...

Spectrum of L

W. Marek, K. Rasmussen

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CONTENTS0. Motivation, results to be used in the sequel ................51. Slicing $L_{α}$ ’s ..........................................................102. Hereditarily countable, definable elements ................133. Spectrum of L.............................................................154. The width of elements of spectrum ............................195. Non-uniform strong definability ..................................266. Solution to a problem of Wilmers................................327....

Fermi Golden Rule, Feshbach Method and embedded point spectrum

Jan Dereziński (1998-1999)

Séminaire Équations aux dérivées partielles

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A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jak $\overset{ˇ}{s}$ ić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.

On the defect spectrum of an extension of a Banach space operator

Vladimír Kordula (1998)

Czechoslovak Mathematical Journal

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Let $T$ be an operator acting on a Banach space $X$ . We show that between extensions of $T$ to some Banach space $Y \supset X$ which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.

Tensor products and Taylor's joint spectrum

Zoia Ceauşescu, F. Vasilescu (1978)

Studia Mathematica

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Topologically Invertible Elements and Topological Spectrum

Mati Abel, Wiesław Żelazko (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x \mapsto x^{- 1}$ is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.

On the left and right joint spectra in Banach algebras

Che-Kao Fong, Andrzej Sołtysiak (1990)

Studia Mathematica

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