Invariant subspaces: continuous stability implies smooth stability
HTML articles powered by AMS MathViewer
- by Lyle Noakes and Kin Yan Chung
- Proc. Amer. Math. Soc. 120 (1994), 119-126
- DOI: https://doi.org/10.1090/S0002-9939-1994-1203990-X
- PDF | Request permission
Abstract:
The stability of an invariant subspace is defined in the terms of the existence of a certain type of function. The imposition of further conditions on this function leads to different forms of stability. Of these, the equivalence of continuous and smooth stability is proved; two proofs are offered for comparison.References
- Kin Yan Chung, Subspaces and graphs, Proc. Amer. Math. Soc. 119 (1993), no. 1, 141–146. MR 1155595, DOI 10.1090/S0002-9939-1993-1155595-6
- I. Gohberg, P. Lancaster, and L. Rodman, Invariant subspaces of matrices with applications, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1986. A Wiley-Interscience Publication. MR 873503
- Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
- P. R. Halmos, Limsups of Lats, Indiana Univ. Math. J. 29 (1980), no. 2, 293–311. MR 563214, DOI 10.1512/iumj.1980.29.29021
- L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute of Mathematical Sciences, New York University, New York, 1974. With a chapter by E. Zehnder; Notes by R. A. Artino; Lecture Notes, 1973–1974. MR 0488102
- Lyle Noakes, Invariant subspaces and perturbations, Proc. Amer. Math. Soc. 114 (1992), no. 2, 365–370. MR 1087467, DOI 10.1090/S0002-9939-1992-1087467-9
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 119-126
- MSC: Primary 47A15; Secondary 15A04
- DOI: https://doi.org/10.1090/S0002-9939-1994-1203990-X
- MathSciNet review: 1203990