On the invertibility of isometric semigroup representations

C. Batty; D. Greenfield

Displaying similar documents to “On the invertibility of isometric semigroup representations”

A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

Charles Batty, Zdzisław Brzeźniak, David Greenfield (1996)

Studia Mathematica

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Let T be a semigroup of linear contractions on a Banach space X, and let $X_{s} (T) = x \in X : l i m_{s \to \infty} ∥ T (s) x ∥ = 0$ . Then $X_{s} (T)$ is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then $X_{s} (T)$ is the annihilator of the unitary eigenvectors of T*, and $l i m_{s} ∥ T (s) x ∥ = i n f ∥ x - y ∥ : y \in X_{s} (T)$ for each x in X.

A spectral theory for locally compact abelian groups of automorphisms of commutative Banach algebras

Sen Huang (1999)

Studia Mathematica

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Let A be a commutative Banach algebra with Gelfand space ∆ (A). Denote by Aut (A) the group of all continuous automorphisms of A. Consider a σ(A,∆(A))-continuous group representation α:G → Aut(A) of a locally compact abelian group G by automorphisms of A. For each a ∈ A and φ ∈ ∆(A), the function $φ_{a} (t) : = φ (α_{t} a)$ t ∈ G is in the space C(G) of all continuous and bounded functions on G. The weak-star spectrum $σ_{w} * (φ_{a})$ is defined as a closed subset of the dual group Ĝ of G. For φ ∈ ∆(A) we define $Ʌ_{φ}^{a}$ to be the...

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...