Operators which are annihilated by analytic functions and invariant subspaces

Atzmon, Aharon

doi:10.1007/bf02392120

Cited by 69 publications

(57 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(i) Soit T un opérateur inversible sur un espace de Banach X vérifiant les conditions (1) et (2). On définit alors le poids ω par…”

Section: Interpolation Dans a St (T ) Et Opérateursunclassified

See 1 more Smart Citation

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Agrafeuil

2005

Studia Math.

View full text Add to dashboard Cite

Abstract. We denote by T the unit circle and by D the unit disc of C. Let s be a non-negative real and ω a weight such that ω(n) = (1 + n) s (n ≥ 0) and the sequence (ω(−n)/(1 + n) s ) n≥0 is non-decreasing. We define the Banach algebraIf I is a closed ideal of A ω (T), we set h 0 (I) = {z ∈ T : f (z) = 0 (f ∈ I)}. We describe all closed ideals I of A ω (T) such that h 0 (I) is at most countable. A similar result is obtained for closed ideals of the algebra A + s (T) = {f ∈ A ω (T) : f (n) = 0 (n < 0)} without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating sets for a ∞ , the space of infinitely differentiable functions in the closed unit disc D and holomorphic in D.

show abstract

“…(i) Soit T un opérateur inversible sur un espace de Banach X vérifiant les conditions (1) et (2). On définit alors le poids ω par…”

Section: Interpolation Dans a St (T ) Et Opérateursunclassified

“…Soit alors µ une mesure continueà support inclu dans F et T µ l'opérateur défini en (24). T µ est une contraction dont le spectre est inclu dans F , et on montre en utilisant le lemme 2 de [2] que…”

unclassified

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Agrafeuil

2005

Studia Math.

View full text Add to dashboard Cite

show abstract

“…")"<=£ is bounded then R = kl (see [1,12]). This result is extended in [2] and [14] to contractions R such that (b') l0g + ||/r"||=0(H5) («->+OO).…”

Section: \\T(t)\\=o(t K+1 ) (T-++oo) (B)mentioning

confidence: 88%

“…and where k > 0 is a given integer? [2] Spectral synthesis and applications to C 0 -groups 129 We prove that if T satisfies the conditions (a)…”

Section: (I) T(0) = / Where / Is the Identity Operator; (Ii) T(t + Smentioning

confidence: 99%

Spectral synthesis and applications to C₀-groups

Zarrabi

1996

J Aust Math Soc A

View full text Add to dashboard Cite

show abstract

“…Next we recall an extension of Gelfand's theorem due to Atzmon [2]: If T ∈ L(X) is invertible and satisfies…”

Section: This Implies (V)mentioning

confidence: 99%

Ditkin’s condition for certain Beurling algebras

Huang

Neerven

Räbiger

1998

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Let G be a locally compact abelian group. A function ω : G → [1, ∞) is said to be a weight if it is locally bounded, Borel measurable and submultiplicative. We call a weight ω on G semi-bounded if there exist a constant K and a subsemigroup S with S − S = G, such that ω(s) ≤ K and limfor all s ∈ S. Using functional analytic methods, we show that all Beurling algebras L 1 ω (G) whose defining weight ω is semi-bounded satisfy Ditkin's condition.

show abstract

Operators which are annihilated by analytic functions and invariant subspaces

Cited by 69 publications

References 14 publications

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Spectral synthesis and applications to C₀-groups

Ditkin’s condition for certain Beurling algebras

Contact Info

Product

Resources

About

Operators which are annihilated by analytic functions and invariant subspaces

Cited by 69 publications

References 14 publications

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Spectral synthesis and applications to C0-groups

Ditkin’s condition for certain Beurling algebras

Contact Info

Product

Resources

About

Spectral synthesis and applications to C₀-groups