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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Oikhberg, Timur 2008. Products of projections in von Neumann algebras. Linear Algebra and its Applications, Vol. 429, Issue. 4, p. 759.

    Kavkler, Iztok 2005. Similarity invariant semigroups generated by non-Fredholm operators. Bulletin of the Australian Mathematical Society, Vol. 72, Issue. 03, p. 407.

    Wu, Pei Yuan 1989. The operator factorization problems. Linear Algebra and its Applications, Vol. 117, p. 35.

    O'Meara, K. C. 1986. Products of idempotents in regular rings. Glasgow Mathematical Journal, Vol. 28, Issue. 02, p. 143.

    Reynolds, M. A. and Sullivan, R. P. 1985. Products of idempotent linear transformations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 100, Issue. 1-2, p. 123.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 94, Issue 3-4
  • January 1983, pp. 351-360

The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space

  • R. J. H. Dawlings (a1)
  • DOI:
  • Published online: 14 November 2011

Let H be a separable Hilbert space and let CL(H) be the semigroup of continuous, linear maps from H to H. Let E+ be the idempotents of CL(H). Let Ker ɑ and Im ɑ be the null-space and range, respectively, of an element ɑ of CL(H) and let St ɑ be the subspace {xH: xɑ = x} of H. It is shown that 〈E+〉 = I∪F∪{i}, where

and ι is the identity map. From the proof it is clear that I and F both form subsemigroups of 〈E+〉 and that the depth of I is 3. It is also shown that the depths of F and 〈E+〉 are infinite.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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