Relative boundedness and relative compactness for linear operators in Banach spaces-Reference-Cited by-同舟云学术

Relative boundedness and relative compactness for linear operators in Banach spaces

Published:2000-03-29 Issue:8 Volume:128 Page:2287-2290
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Binding P.,Hryniv R.

Abstract

If A A and B B are linear operators acting between Banach spaces, we show that compactness of B B relative to A A does not in general imply that B B has A A -bound zero. We do, however, give conditions under which the above implication is valid.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2000-128-08/S0002-9939-00-05729-4/S0002-9939-00-05729-4.pdf

Reference7 articles.

1. Grundlehren der Mathematischen Wissenschaften, Band 132;Kato, Tosio,1976

2. North-Holland Series in Applied Mathematics and Mechanics, Vol. 14;Schechter, Martin,1971

3. On the spectrum of singular boundary-value problems;Birman, M. Š.;Mat. Sb. (N.S.),1961

4. Damped vibrations of beams and related spectral problems;Lancaster, Peter;Canad. Appl. Math. Quart.,1994

5. Binding, P., Hryniv, R., Langer, H., Najman, B. Elliptic eigenvalue problems with eigenparameter dependent boundary conditions, to appear.

Cited by 21 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Trotter-Kato Product Formulæ: Operator-Norm Topology;Operator Theory: Advances and Applications;2024

2. FUNCTIONAL MODEL FOR BOUNDARY‐VALUE PROBLEMS;Mathematika;2021-05-07

3. The 3D transient semiconductor equations with gradient-dependent and interfacial recombination;Mathematical Models and Methods in Applied Sciences;2019-09

4. Relatively Bounded and Relatively Compact Perturbations for Limit Circle Hamiltonian Systems;Integral Equations and Operator Theory;2016-10-21

5. Applications in Mathematical Physics and Biology;Spectral Theory and Applications of Linear Operators and Block Operator Matrices;2015