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A Geometric Characterization of Nonnegative Bands
Published online by Cambridge University Press: 20 November 2018
Abstract
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A band is a semigroup of idempotent operators. A nonnegative band 
$\mathcal{S}$ in 
$B({{L}^{2}}(X))$ having at least one element of finite rank and with rank 
$(S)\,>\,1$ for all 
$S$ in $\mathcal{S}$ is known to have a special kind of common invariant subspace which is termed a standard subspace (defined below).
Such bands are called decomposable. Decomposability has helped to understand the structure of nonnegative bands with constant finite rank. In this paper, a geometric characterization of maximal, rank-one, indecomposable nonnegative bands is obtained which facilitates the understanding of their geometric structure.
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- Research Article
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- Copyright
- Copyright © Canadian Mathematical Society 2004
References
[1]
Choi, M. D., Nordgren, E. A., Radjavi, H., Rosenthal, P. and Zhong, Y., Triangularizing semigroups of quasinilpotent operators with nonnegative entries. Indiana Univ.Math. J. 42 (1993), 15–25.Google Scholar
[2]
Fillmore, P., MacDonald, G., Radjabalipour, M., and Radjavi, H., Towards a classification of maximal unicellular bands. Semigroup Forum 49 (1994), 195–215.Google Scholar
[3]
Fillmore, P., MacDonald, G., Radjabalipour, M., and Radjavi, H., On principal-ideal bands. Semigroup Forum, to appear.Google Scholar
[4]
Marwaha, A., Decomposability and structure of nonnegative bands in infinite dimensions. J. Operator Theory 47 (2002), 37–61.Google Scholar
[5]
Radjavi, H., On reducibility of semigroups of compact operators. Indiana Univ.Math. J. 39 (1990), 499–515.Google Scholar
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