Quasi-constricted linear operators on Banach spaces

2001-01-01
Wolff, MPH
Emel'yanov, Eduard Yu.
Let X be a Banach space over C. The bounded linear operator T on X is called quasi-constricted if the subspace X-0 := {x epsilon X : lim(n --> infinity) parallel toT(n)x parallel to = 0} is closed and has finite codimension. We show that a power bounded linear operator T epsilon L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness chi parallel to (.)parallel to (1) (A) )over bar>T is mean ergodic for all lambda in the peripheral spectrum sigma (pi)(T) of T is constricted and power bounded, and hence has a compact attractor.
STUDIA MATHEMATICA

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Citation Formats
M. Wolff and E. Y. Emel’yanov, “Quasi-constricted linear operators on Banach spaces,” STUDIA MATHEMATICA, vol. 144, no. 2, pp. 169–179, 2001, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94903.