1994-06-01
Zero sums of idempotents in Banach algebras
Publication
Publication
Integral Equations and Operator Theory , Volume 19 - Issue 2 p. 125- 134
The problem treated in this paper is the following. Let p1,..., pkbe idempotents in a Banach algebra B, and assume p1+...+pk=0. Does it follow that pj=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.
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| , , , | |
| doi.org/10.1007/BF01206409, hdl.handle.net/1765/73119 | |
| Integral Equations and Operator Theory | |
| Organisation | Erasmus School of Economics |
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Bart, H., Ehrhardt, T., & Silbermann, B. (1994). Zero sums of idempotents in Banach algebras. Integral Equations and Operator Theory, 19(2), 125–134. doi:10.1007/BF01206409 |
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