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On idempotent affine mappings

  • R. J. H. Dawlings (a1)

Synopsis

Let V be a vector space and End (V) the semigroup of endomorphisms of V. An affine mapping of V is a map A: VV given by xA = xα + a, where a belongs to End (V) and a is some element of V. Let (V) be the semigroup of affine mappings of V.

Let E' denote the non-injective idempotents of End (V) and let ℰ denote the idempotents of (V). In this paper 〈ℰ〉 is determined in terms of 〈E′〉 when End (V) consists of all endomorphisms of V and when End (V) only contains the continuous endomorphisms (in which case we restrict V to being an inner product space).

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References

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1Dawlings, R. J. H.. Semigroups of Singular Endomorphisms of Vector Spaces (St Andrews Univ. Ph.D. Thesis, 1980).
2Dawlings, R. J. H.. The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space. Proc. Roy. Soc. Edinburgh Sect. A, to appear.
3Erdos, J. A.. On products of idempotent matrices. Glasgow Math. J. 8 (1967), 118122.

On idempotent affine mappings

  • R. J. H. Dawlings (a1)

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