Displaying similar documents to “A spectral theory for locally compact abelian groups of automorphisms of commutative Banach algebras”

Three spectral notions for representations of commutative Banach algebras

Yngve Domar, Lars-Ake Lindahl (1975)

Annales de l'institut Fourier

Similarity:

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 - b ^ ( φ ) x ∥ < ϵ ∥ x ∥ , b ∈ F , have a common solution x ≠ 0 , for any ϵ > 0 and any finite subset F of B . A theorem of Beurling on the spectrum of L ∞ -functions and results of Slodkowski and Zelazko on joint topological divisors of zero appear as special cases of...

On the invertibility of isometric semigroup representations

C. Batty, D. Greenfield (1994)

Studia Mathematica

Similarity:

Let T be a representation of a suitable abelian semigroup S by isometries on a Banach space. We study the spectral conditions which will imply that T(s) is invertible for each s in S. On the way we analyse the relationship between the spectrum of T, Sp(T,S), and its unitary spectrum S p u ( T , S ) . For S = ℤ + n or ℝ + n , we establish connections with polynomial convexity.

Perturbation and spectral discontinuity in Banach algebras

Rudi Brits (2011)

Studia Mathematica

Similarity:

We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite-dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to show that given any Banach algebra, Y, one may adjoin to Y a non-commutative inessential ideal, I, so that in the resulting algebra, A, the following holds: To each x ∈ Y whose spectrum separates the plane there corresponds a perturbation of x, of...

On the joint spectral radius

Vladimír Müller (1997)

Annales Polonici Mathematici

Similarity:

We prove the p -spectral radius formula for n-tuples of commuting Banach algebra elements

On a certain class of subspectra

Andrzej Sołtysiak (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting n -tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.