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Topics in Modern Operator Theory pp 105–120Cite as

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Commutants Modulo the Compact Operators of Certain CSL Algebras

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 2))

Abstract

In recent years several papers have appeared which focus on the structure of the commutant modulo compacts or essential commutant of certain algebras of operators on Hilbert space. For von Neumann algebras B. Johnson and S. Parrott [6]have shown that for all, but possibly ones containing certain type II1 direct summands, the essential commutant is the algebraic commutant plus the compact operators. Subsequently characterizations have been given for the essential commutant of the analytic Toeplitz ope-rators [3], nest algebras [2] and nest subalgebras of von Neumann algebras [4].

Partially supported by the National Science Foundation.

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References

  1. Arveson, W.: Operator algebras and invariant subspaces, Ann. of Math. 100 (1974), 433–532.

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  2. Christensen, E.; Peligrad, C.: Commutants of nest algebras modulo the compact operators, preprint.

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  3. Davidson, K.R.: On operators commuting with Toeplitz operators modulo the compact operators, J. Functional Analysis 24 (1977), 291–302.

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  4. Gilfeather, F.; Larson, D.R.: Nest subalgebras of von Neumann algebras: Commutants modulo compacts and distance estimates, preprint.

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  5. Fillmore, P.A.; Stampfli, J.G.; Williams, J.P.: On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179–192.

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  6. Johnson, B.E.; Parrott, S.K.: Operators commuting with a von Neumann algebra modulo the set of compact operators, J. Functional Analysis 11 (1972), 39–61.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska, 68588, USA

    Frank Gilfeather & David R. Larson

Authors
  1. Frank Gilfeather
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  2. David R. Larson
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Editors and Affiliations

  1. Department of Mathematics, INCREST, Bd. Pacii 220, 79622, Bucharest, Romania

    C. Apostol , R. G. Douglas , B. Sz.- Nagy , D. Voiculescu  & Gr. Arsene , , ,  & 

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© 1981 Springer Basel AG

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Gilfeather, F., Larson, D.R. (1981). Commutants Modulo the Compact Operators of Certain CSL Algebras. In: Apostol, C., Douglas, R.G., Nagy, B.S., Voiculescu, D., Arsene, G. (eds) Topics in Modern Operator Theory. Operator Theory: Advances and Applications, vol 2. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5456-6_9

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  • DOI: https://doi.org/10.1007/978-3-0348-5456-6_9

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1244-2

  • Online ISBN: 978-3-0348-5456-6

  • eBook Packages: Springer Book Archive

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