A resolvent condition implying power boundedness

Nagy, B.; Zemánek, Jaroslav

doi:10.4064/sm-134-2-143-151

Cited by 71 publications

(62 citation statements)

References 19 publications

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“…It was then observed independently in 1998 by B. Nagy and J. Zemánek [9], O. Nevanlinna, and Yu. Lyubich [6] that if (1) holds for all |λ| > 1, then (1), indeed, holds for all λ ∈ K δ ∪ D c for some δ > 0 (with another possibly larger constantC in place for C).…”

Section: Introductionmentioning

confidence: 82%

On a Tauberian Condition for Bounded Linear Operators

Malinen¹,

Nevanlinna²,

Yuan³

2009

Mathematical Proceedings of the Royal Irish Academy

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Section: Introductionmentioning

confidence: 82%

On a Tauberian Condition for Bounded Linear Operators

Malinen¹,

Nevanlinna²,

Yuan³

2009

Mathematical Proceedings of the Royal Irish Academy

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“…Given ϕ ∈ (0, π/2), we first claim that there is a c 0 ≥ 1 depending only on ϕ, M 0 , M 1 such that (11) sup{…”

Section: 4])mentioning

confidence: 99%

On an integral of fractional power operators

Dungey

2009

Colloq. Math.

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Abstract. For a bounded and sectorial linear operator V in a Banach space, with spectrum in the open unit disc, we study the operator e V = ∞ 0 dα V α . We show, for example, that e V is sectorial, and asymptotically of type 0. If V has single-point spectrum {0}, then e V is of type 0 with a single-point spectrum, and the operator I − e V satisfies the Ritt resolvent condition. These results generalize an example of Lyubich, who studied the case where V is a classical Volterra operator.

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“…The following characterization of operators satisfying Ritt's condition is due to Nagy and Zemánek [15] and Lyubich [13]. THEOREM 2.1.…”

Section: Preliminariesmentioning

confidence: 99%

“…See [16]. [15] Regularity of power-bounded operators 359 THEOREM 4.5. Let X be a GT-space (for example, X = L 1 , 1 or X = L 1 /H 1 ).…”

Section: Proof From (44) We Deduce Thatmentioning

confidence: 99%

Remarks on ℓ1 and -Maximal Regularity for Power-Bounded Operators

Kalton¹,

Portal²

2008

JAZ

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We discuss p -maximal regularity of power-bounded operators and relate the discrete to the continuous time problem for analytic semigroups. We give a complete characterization of operators with 1 and ∞ -maximal regularity. We also introduce an unconditional form of Ritt's condition for power-bounded operators, which plays the role of the existence of an H ∞ -calculus, and give a complete characterization of this condition in the case of Banach spaces which are L 1 -spaces, C(K )-spaces or Hilbert spaces.2000 Mathematics subject classification: 47A30, 47A60, 47D06, 39A12.

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A resolvent condition implying power boundedness

Cited by 71 publications

References 19 publications

On a Tauberian Condition for Bounded Linear Operators

On a Tauberian Condition for Bounded Linear Operators

On an integral of fractional power operators

Remarks on ℓ1 and -Maximal Regularity for Power-Bounded Operators

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