TY - JOUR
T1 - Weakly /pstable linear operators are power stable
AU - Weiss, Groege
PY - 1989/11
Y1 - 1989/11
N2 - We prove that if a bounded linear operator A on a Banach space X is such that, for any x ε X and any y ε X*, the sequence ⟨Ak.x, y,⟩ is in; is in lpwhere p ε (1, ∞), then the spectral radius of A is smaller than one. This solves the discrete-time version of a problem raised by Pritchard and Zabczyk (1983). As a consequence, if the linear time-invariant discrete-time systems associated with A are lq-input-bounded state stable, where qε(1,∞), then A is power stable.
AB - We prove that if a bounded linear operator A on a Banach space X is such that, for any x ε X and any y ε X*, the sequence ⟨Ak.x, y,⟩ is in; is in lpwhere p ε (1, ∞), then the spectral radius of A is smaller than one. This solves the discrete-time version of a problem raised by Pritchard and Zabczyk (1983). As a consequence, if the linear time-invariant discrete-time systems associated with A are lq-input-bounded state stable, where qε(1,∞), then A is power stable.
UR - http://www.scopus.com/inward/record.url?scp=0024771490&partnerID=8YFLogxK
U2 - 10.1080/00207728908910309
DO - 10.1080/00207728908910309
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AN - SCOPUS:0024771490
SN - 0020-7721
VL - 20
SP - 2323
EP - 2328
JO - International Journal of Systems Science
JF - International Journal of Systems Science
IS - 11
ER -