Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Strong connectedness of the invertibles in a finite subdiagonal algebra

Authors: Michael Marsalli and Graeme West
Journal: Proc. Amer. Math. Soc. 128 (2000), 2967-2972
MSC (2000): Primary 46L52
Published electronically: April 7, 2000
MathSciNet review: 1670403
Full-text PDF

Abstract | References | Similar Articles | Additional Information


Suppose $H^\infty$ is a finite, subdiagonal subalgebra of a von Neumann algebra. We show that the invertible group of $H^\infty$ is strongly connected.

References [Enhancements On Off] (What's this?)

  • 1. T. Ando, Comparison of norms of $\Vert f(A) - f(B)\Vert$ and $\Vert f(\vert A-B\vert)\Vert$, Math. Z. 197 (1988), 403-409. MR 90a:47021
  • 2. W. Arveson, Analyticity in operator algebras, Amer. J. Math. 89 (1967), 578-642. MR 36:6946
  • 3. K. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific and Technical, 1988. MR 90f:47062
  • 4. K. Davidson and J. Orr, The invertibles are connected in infinite multiplicity nests, Bull. London Math. Soc. 27 (1995), 155-161. MR 96c:47062
  • 5. K. Davidson, J. Orr, and D. Pitts, Connectedness of the invertibles in certain nest algebras, Can. Math. Bull. 38 (1995), 412-420. MR 96m:47088
  • 6. P. Dodds and T. Dodds, On a submajorisation inequality of T. Ando, Operator Theory in Function Spaces and Banach Lattices (C.B. Huÿsmans et al., ed.), Operator Theory Advances and Applications, vol. 75, Birkhäuser/Springer-Verlag, Basel/Boston/Berlin, 1995, pp. 113-131. MR 96b:47003
  • 7. T. Fack and H. Kosaki, Generalised s-numbers of $\tau$-measurable operators, Pacific J. Math. 123 (1986), 269-300. MR 87h:46122
  • 8. R. Kadison and J. Ringrose, Fundamentals of the theory of operator algebras. Volume I: Elementary theory. Volume II: Advanced theory, Pure and Applied Mathematics, Academic Press, London, 1983, 1986. MR 85j:46099; MR 88d:46106
  • 9. G. Knowles and R. Saeks, On the structure of invertible operators in a nest-subalgebra of a von Neumann algebra, Topics in Operator Theory Systems and Networks (Rehovot, 1983), Operator Theory Advances and Applications, vol. 12, Birkhäuser, Basel/Boston,1984, pp. 303-317. MR 86c:47064
  • 10. M. Marsalli, Noncommutative $H^2$ spaces, Proc. Amer. Math. Soc. 125 (1997), 779-784. MR 97e:46089
  • 11. M. Marsalli and G. West, Noncommutative $H^p$ spaces, J. Operator Theory 40 (1998), 339-355. CMP 99:04
  • 12. M. McAsey, P. Muhly, and K.-S. Saito, Nonselfadjoint crossed products (invariant subspaces and maximality), Trans. Amer. Math. Soc. 248 (1979), 381-409. MR 80j:46101b
  • 13. R. Powers and E. Størmer, Free states of the canonical anticommutation relations, Comm. Math. Phys. 16 (1970), 1-33. MR 42:4126
  • 14. K.-S. Saito, A note on invariant subspaces for finite maximal subdiagonal algebras, Proc. Amer. Math. Soc. 77 (1979), 348-352. MR 81b:46078

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L52

Retrieve articles in all journals with MSC (2000): 46L52

Additional Information

Michael Marsalli
Affiliation: Department of Mathematics, Campus Box 4520, Illinois State University, Normal, Illinois 61790-4520

Graeme West
Affiliation: Department of Mathematics, University of the Witwatersrand, 2050 WITS, South Africa

Keywords: von Neumann algebra, finite subdiagonal algebras
Received by editor(s): June 15, 1998
Received by editor(s) in revised form: November 22, 1998
Published electronically: April 7, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society