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A Geometric Characterization of Nonnegative Bands

Published online by Cambridge University Press:  20 November 2018

Alka Marwaha
Alka Marwaha*
Affiliation:
Department of Mathematics Jesus and Mary College (University of Delhi) Chanakyapuri New Delhi - 110 021 India, email: [email protected]
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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.

Keywords

47D0347A15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 257 - 263
Copyright
Copyright © Canadian Mathematical Society 2004

References

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