Taiwanese Journal of Mathematics

STRONGLY CONTINUOUS GROUPS, SIMILARITY AND NUMERICAL RANGE ON A HILBERT SPACE

Ralph deLaubenfels

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Abstract

It is shown that $iB$ generates a strongly continuous group of exponential type $\omega$ on a Hilbert space if and only if for all $\alpha \gt \omega$, $B$ is similar to an operator with spectrum and numerical range contained in the horizontal strip $\{z \in {\bf C} \, | \, |Im(z)| \lt \alpha \}$.

Article information

Source
Taiwanese J. Math., Volume 1, Number 2 (1997), 127-133.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405229

Digital Object Identifier
doi:10.11650/twjm/1500405229

Mathematical Reviews number (MathSciNet)
MR1452089

Subjects
Primary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A12: Numerical range, numerical radius 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 47A60: Functional calculus

Keywords
groups of operators numerical range $H^\infty$ functional calculi

Citation

deLaubenfels, Ralph. STRONGLY CONTINUOUS GROUPS, SIMILARITY AND NUMERICAL RANGE ON A HILBERT SPACE. Taiwanese J. Math. 1 (1997), no. 2, 127--133. doi:10.11650/twjm/1500405229. https://projecteuclid.org/euclid.twjm/1500405229


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