Taiwanese Journal of Mathematics

MEAN STABILITY OF SEMIGROUPS

Shmuel Kantorovitz and Serguei Piskarev

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Abstract

Let $T(\cdot)$ be a bounded $C_0$-semigroup on the Banach space $X$, with generator $A$. It is shown that the denseness of range $A$ is necessary and sufficient for the semigroup's mean stability with respect to suitable weights. Analogous results are valid for power bounded operators, tensor product semigroups, and cosine operator functions.

Article information

Source
Taiwanese J. Math., Volume 6, Number 1 (2002), 89-103.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407402

Digital Object Identifier
doi:10.11650/twjm/1500407402

Mathematical Reviews number (MathSciNet)
MR1884457

Zentralblatt MATH identifier
1041.47021

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 47D09: Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10] 47D60: $C$-semigroups, regularized semigroups

Keywords
mean stability semigroup generator point spectrum residual spectrum c-semigroup tensor product of semigroups power bounded operator cosine operator function

Citation

Kantorovitz, Shmuel; Piskarev, Serguei. MEAN STABILITY OF SEMIGROUPS. Taiwanese J. Math. 6 (2002), no. 1, 89--103. doi:10.11650/twjm/1500407402. https://projecteuclid.org/euclid.twjm/1500407402


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