Quasi constricted linear representations of abelian semigroups on Banach spaces

Date

2002-07-24

Author

Emelyanov, Eduard

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

96
views

0
downloads

Let (X, ∥·∥) be a Banach space. We study asymptotically bounded quasi constricted representations of an abelian semigroup IP in L(X), i.e. representations (Tt)t∈IP which satisfy the following conditions: i) limt→∞ ∥Ttx∥ < ∞ for all x ∈ X. ii) X0:= {x ∈ X:limt→∞ ∥Ttx∥ = 0} is closed and has finite codimension. We show that an asymptotically bounded representation (Tt)t∈IP is quasi constricted if and only if it has an attractor A with Hausdorff measure of noncompactness X∥·∥1 (A) < 1 with respect to some equivalent norm ∥·∥1 on X. Moreover we prove that every asymptotically weakly almost periodic quasi constricted representation (Tt)t∈IP is constricted, i.e. there exists a finite dimensional (Tt)t∈IP-invariant subspace Xr such that X:= X0 ⊕ Xr. We apply our results to C0-semigroups.

Subject Keywords

C0-semigroups, Constricted semigroups, Quasi-constricted semi-groups, Semigroups of operators, Weakly almost periodic semigroups

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=0036067338&origin=inward
https://hdl.handle.net/11511/94774

Journal

Mathematische Nachrichten

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Quasi-constricted linear operators on Banach spaces Wolff, MPH; Emel'yanov, Eduard Yu. (2001-01-01) 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 constric...
On local finiteness of periodic residually finite groups Kuzucouoglu, M; Shumyatsky, P (2002-10-01) Let G be a periodic residually finite group containing a nilpotent subgroup A such that C-G (A) is finite. We show that if [A, A(g)] is finite for any g is an element of G, then G is locally finite.
Some conditions for a co-semigroup to be asymptotically finite-dimensional Emelyanov, Eduard (2003-09-01) We study the class of bounded C-0-semigroups T = (T-t)(tgreater than or equal to0) on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X-0(T) infinity)parallel toT(t)xparallel to = 0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.
Value sets of folding polynomials over finite fields Küçüksakallı, Ömer (2019-01-01) Let k be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra g. We find the cardinality of the value sets of the folding polynomials P-g(k)(x) is an element of Z[x] of arbitrary rank n >= 1, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
On characterization of a Riesz homomorphism on C(X)-space AKKAR ERCAN, ZÜBEYDE MÜGE; Önal, Süleyman (Informa UK Limited, 2007-06-01) Let X be a realcompact space. We present a very simple and elementary proof of the well known fact that every Riesz homomorphism pi : C(X) -> R is point evaluated. Moreover, the proof is given in ZF.

Citation Formats

E. Emelyanov, “Quasi constricted linear representations of abelian semigroups on Banach spaces,” Mathematische Nachrichten, vol. 233-234, pp. 103–110, 2002, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=0036067338&origin=inward.