A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

• Autorzy: Charles J. K. Batty , Zdzisław Brzeźniak , David A. Greenfield
• Języki publikacji: EN

Abstrakty

EN

Let T be a semigroup of linear contractions on a Banach space X, and let $X_{s}(T) = {x ∈ X : lim_{s→∞} ∥T(s)x∥ = 0}$. 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 $lim_{s} ∥T(s)x∥ = inf{∥x-y∥ : y ∈ X_{s}(T)}$ for each x in X.

Słowa kluczowe

EN

contraction semigroup; unitary spectrum; unitary eigenvector trajectory; asymptotic stability; trivially asymptotically stable; countable; spectral synthesis

Kategorie tematyczne

• 47D03: Groups and semigroups of linear operators
• 35B40: Asymptotic behavior of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 2
• Strony: 167-183

Daty

wydano

1996

otrzymano

1996-01-15

poprawiono

1996-07-15

Twórcy

autor

Charles J. K. Batty

• St. John's College, Oxford OX1 3JP, England,

autor

Zdzisław Brzeźniak

• Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, England

autor

David A. Greenfield

• 87 Eversley Road, Benfleet, Essex SS7 4JT, England

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