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

DOI:
https://doi.org/10.1090/S0002-9939-03-07217-4

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 on a complex Banach space and a closed subset of the complex plane this note deals with algebraic representations of the corresponding analytic spectral subspace from local spectral theory. If is the restriction of a generalized scalar operator to a closed invariant subspace, then it is shown that for all sufficiently large integers where denotes the largest linear subspace of for which for all Moreover, for a wide class of operators that satisfy growth conditions of polynomial or Beurling type, it is shown that is closed and equal to

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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:
https://doi.org/10.1090/S0002-9939-03-07217-4

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