Quasi-constricted linear operators on Banach spaces

Date

2001-01-01

Author

Wolff, MPH
Emel'yanov, Eduard Yu.

Metadata

Show full item record

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

Item Usage Stats

166
views

2
downloads

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.

URI

https://hdl.handle.net/11511/94903

Journal

STUDIA MATHEMATICA

DOI

https://doi.org/10.4064/sm144-2-5

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Invariant subspaces for Banach space operators with an annular spectral set Yavuz, Onur (2008-01-01) Consider an annulus Omega = {z epsilon C : r(0) 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).
Invariant densities and mean ergodicity of Markov operators Emelyanov, Eduard (2003-01-01) We prove that a, Markov operator T on L-1 has an invariant density if and only if there exists a density f that satisfies lim sup(n-->infinity) parallel toT(n) f-fparallel to infinity) parallel toP(n)f - wparallel to < 2 for every density f. Corresponding results hold for strongly continuous semigroups.
Piecewise polynomials with different smoothness degrees on polyhedral complexes ALTINOK BHUPAL, SELMA; Sipahi, Neslihan Os (Informa UK Limited, 2019-05-01) For a given d-dimensional polyhedral complex Delta and a given degree k, we consider the vector space of piecewise polynomial functions on Delta of degree at most k with a different smoothness condition on each pair of adjacent d-faces of Delta. This is a finite dimensional vector space. The fundamental problem in Approximation Theory is to compute the dimension of this vector space. It is known that the dimension is given by a polynomial for sufficiently large k via commutative algebra. By using the techni...
Almost periodic solutions of the linear differential equation with piecewise constant argument Akhmet, Marat (2009-10-01) The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01) Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...

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.