scholarly journals Non-power bounded generators of strongly continuous semigroups

2016 ◽  
Vol 436 (1) ◽  
pp. 429-438 ◽  
Author(s):  
Anna Golińska ◽  
Sven-Ake Wegner
Keyword(s):  
Strongly Continuous Semigroups ◽  
Power Bounded

scholarly journals Lipschitz stratifications in power-bounded $o$-minimal fields

2018 ◽  
Vol 20 (11) ◽  
pp. 2717-2767 ◽  
Author(s):  
Immanuel Halupczok ◽  
Yimu Yin
Keyword(s):  
Power Bounded

Two Consequences of Brunel's Theorem

1991 ◽  
Vol 34 (1) ◽  
pp. 105-108
Author(s):  
James H. Olsen
Keyword(s):  
Ergodic Theorem ◽  
Bounded Operators ◽  
Positive Power ◽  
Multiple Sequence ◽  
Power Bounded Operators ◽  
Recent Theorem ◽  
The Individual ◽  
Power Bounded

AbstractIn this note we observe two consequences of Brunei's recent theorem. If T1,..., Tn are majorized by positive power-bounded operators S1,..., Sn of Lp, 1 < p < ∞, for which the ergodic theorem holds, then a multiple sequence ergodic theorem holds for T1,....,Tn. Further, the individual convergence for each Tk can be taken along uniform sequences.

scholarly journals On power-bounded prespectral operators

1976 ◽  
Vol 20 (2) ◽  
pp. 173-175
Author(s):  
H. R. Dowson
Keyword(s):  
Growth Condition ◽  
Bounded Operator ◽  
Spectral Operator ◽  
Scalar Type ◽  
Image Position ◽  
Power Bounded Operator ◽  
Power Bounded

Foguel (8) and Fixman (7) independently proved that an invertible spectral operator, which is power-bounded, is of scalar type. Their proofs rely heavily on a result of Dunford on spectral operators whose resolvents satisfy a growth condition. (See Lemma 3.16 of (6, p. 609).) Observe that the resolvent of an invertible power-bounded operator T satisfies an inequality of the form

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