The Case for Cross-Component Power Coordination on Power Bounded Systems

2021 ◽  
pp. 1-1
Author(s):  
Rong Ge ◽  
Xizhou Feng ◽  
Tyler Allen ◽  
Pengfei Zou
Keyword(s):  
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

Biholomorphic Mappings on Banach Spaces

2019 ◽  
Vol 62 (4) ◽  
pp. 913-924
Author(s):  
H. Carrión ◽  
P. Galindo ◽  
M. L. Lourenço
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Open Subset ◽  
Separable Hilbert Space ◽  
Derivative Operator ◽  
Infinite Dimensional ◽  
Dimensional Version ◽  
Dual Banach Space ◽  
Bounded Convex ◽  
Power Bounded

AbstractWe present an infinite-dimensional version of Cartan's theorem concerning the existence of a holomorphic inverse of a given holomorphic self-map of a bounded convex open subset of a dual Banach space. No separability is assumed, contrary to previous analogous results. The main assumption is that the derivative operator is power bounded, and which we, in turn, show to be diagonalizable in some cases, like the separable Hilbert space.

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