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Zero sums of idempotents in Banach algebras.
- Source :
- Integral Equations & Operator Theory; Jun1994, Vol. 19 Issue 2, p125-134, 10p
- Publication Year :
- 1994
-
Abstract
- The problem treated in this paper is the following. Let p,..., p be idempotents in a Banach algebra B, and assume p+...+ p=0. Does it follow that p=0, j=1,..., k? For important classes of Banach algebras the answer turns out to be positive; in general, however, it is negative. A counterexample is given involving five nonzero bounded projections on infinite-dimensional separable Hilbert space. The number five is critical here: in Banach algebras nontrivial zero sums of four idempotents are impossible. In a purely algebraic context (no norm), the situation is different. There the critical number is four. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0378620X
- Volume :
- 19
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Integral Equations & Operator Theory
- Publication Type :
- Academic Journal
- Accession number :
- 70859939
- Full Text :
- https://doi.org/10.1007/BF01206409