ISSN:
1420-8989
Keywords:
Primary 16A32
;
16A38
;
46H99
;
Secondary 45E05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The problem treated in this paper is the following.Let p 1,...,p k be idempotents in a Banach algebra B, and assume p 1+...+p k =0.Does it follow that p j =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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01206409
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