Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
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
133
views
0
downloads
Cite This
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
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.