Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral subspaces of subscalar and related operators


Authors: T. L. Miller, V. G. Miller and M. M. Neumann
Journal: Proc. Amer. Math. Soc. 132 (2004), 1483-1493
MSC (2000): Primary 47A11; Secondary 47B37, 47B40
Published electronically: October 3, 2003
MathSciNet review: 2053356
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a bounded linear operator $T\in L(X)$ on a complex Banach space $X$ and a closed subset $F$ of the complex plane $\mathbb{C},$ this note deals with algebraic representations of the corresponding analytic spectral subspace $ X_{T}(F)$ from local spectral theory. If $T$ is the restriction of a generalized scalar operator to a closed invariant subspace, then it is shown that $X_{T}(F)=E_{T}(F)=\bigcap_{\hspace{0.03cm}\lambda \notin F}\left( \lambda -T\right) ^{\hspace{0.03cm}p}X$ for all sufficiently large integers $ p,$ where $E_{T}(F)$ denotes the largest linear subspace $Y$ of $X$ for which $\left( \lambda -T\right) Y=Y$ for all $\lambda \in \mathbb{C} \setminus F.$ Moreover, for a wide class of operators $T$ that satisfy growth conditions of polynomial or Beurling type, it is shown that $X_{T}(F)$is closed and equal to $E_{T}(F).$


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A11, 47B37, 47B40

Retrieve articles in all journals with MSC (2000): 47A11, 47B37, 47B40


Additional Information

T. L. Miller
Affiliation: Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, Mississippi State, Mississippi 39762
Email: miller@math.msstate.edu

V. G. Miller
Affiliation: Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, Mississippi State, Mississippi 39762
Email: vivien@math.msstate.edu

M. M. Neumann
Affiliation: Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, Mississippi State, Mississippi 39762
Email: neumann@math.msstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07217-4
PII: S 0002-9939(03)07217-4
Received by editor(s): August 22, 2002
Received by editor(s) in revised form: January 14, 2003
Published electronically: October 3, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society