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Journal of Operator Theory

Volume 47, Issue 1, Winter 2002  pp. 37-61.

Decomposability and structure of nonnegative bands in infinite dimensions

Authors:  Alka Marwaha
Author institution: Department of Mathematics, Jesus and Mary College, (University of Delhi), Chanakyapuri, New Delhi-110021, New Delhi-110021, India

Summary:  A semigroup in $\calb(\call^2(\calx))$ is a collection of operators which is closed under multiplication. A band will denote a semigroup of idempotents. The question whether a band of infinite-rank operators on an infinite-dimensional Hilbert space is reducible is still unsolved. Here, a negative answer to this problem is given as far as decomposability of a band is concerned. Furthermore, conditions leading to decomposability of such bands are discussed. Also, the structure of a maximal nonnegative band of constant rank $r$ is given is under special condition.

Keywords:  Semigroups, decomposability, standard subspaces and bands

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