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Proceedings of the American Mathematical Society

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Spans and intersections of essentially reducing subspaces

Author: Michael J. Hoffman
Journal: Proc. Amer. Math. Soc. 72 (1978), 333-340
MSC: Primary 47A15
MathSciNet review: 507334
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Abstract: If P and Q are the projections onto essentially reducing subspaces M and N for an operator, the closed linear span and the intersection of M and N need not be essentially reducing or even essentially invariant. However, they are if $ M + N$ is closed, in particular if $ PQ = QP$ or if PQ is compact.

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  • [1] W. B. Arveson, Notes on extensions of $ {C^\ast}$-algebras, Duke Math. J. 44 (1977), 329-355. MR 0438137 (55:11056)
  • [2] J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. 42 (1941), 839-873. MR 0005790 (3:208c)
  • [3] J. Dixmier, Etude sur les variétés et les opérateurs de Julia, Bull. Soc. Math. France 77 (1949), 11-101. MR 0032937 (11:369f)
  • [4] P. A. Fillmore, J. G. Stampfli and J. P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179-192. MR 0322534 (48:896)
  • [5] P. A. Fillmore and J. P. Williams, On operator ranges, Advances in Math. 7 (1971), 254-281. MR 0293441 (45:2518)
  • [6] B. Simon, Geometric methods in multiparticle quantum systems, Comm. Math. Phys. 55 (1977), 259-274. MR 0496073 (58:14691a)
  • [7] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), 97-113. MR 0415338 (54:3427)

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Keywords: Essentially invariant subspaces, essentially reducing subspaces, compact perturbations, Calkin algebra
Article copyright: © Copyright 1978 American Mathematical Society

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