Skip to main content
SpringerLink
Log in

Factorization along commutative subspace lattices

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

A positive invertible operatorT is said to be factorable along a commutative subspace latticeL if there is an invertible operatorA inAlg L whose inverse is also inAlg L and such thatT=A*A. We investigate a number of conditions that are equivalent to factorability of a given operator along a latticeL. As a byproduct, we derive a condition that guarantees that the latticeT L, defined as {range(TE) ∶E ∈L} is commutative. Applications are suggested to the particular case of factoringL ∞ functions via analytic Toeplitz operators on the polydisc.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. Arveson,Interpolation Problems in Nest Algebras, Journal of Functional Analysis20 (1975), 208–233.

    Google Scholar 

  2. J. Daughtry,Factorizations along commutative subspace lattices, Integral Equations and Operator Theory10 (1987), 290–296.

    Google Scholar 

  3. J. Daughtry and R. Johns,Arveson Nests and Operator Factorization along Commutative Subspace Lattices, Proceedings of the American Mathematical Society107, number 4 (Dec. 1989), 943–947.

    Google Scholar 

  4. K. Hoffman,Banach Space of Analytic Functions, Prentice-Hall, 1962.

  5. E. Katsoulis, R. Moore, and T. Trent,Interpolation in Nest Algebras and Applications to Operator Corona Theorems, to appear, Journal of Operator Theory.

  6. D. Larson,Nest Algebras and Similarity Transformations, Annals of Mathematics121 (1985), 409–427.

    Google Scholar 

  7. D. Pitts,Factorization Problems for Nests: Factorization Methods and Characterizations of the Universal Factorization Property, Journal of Functional Analysis79, no. 1 (July 1988), 57–90.

    Google Scholar 

  8. G. Pólya and G. Szegö,Aufgaben und Lehrsätze aus der Analysis Heidelberger Tasenbücher Band 74, Springer-Verlag, 1971.

  9. W. Rudin,Function Theory in Polydiscs, W. A. Benjamin, 1969.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Alabama, 35487-0350, Tuscaloosa, AL

    R. L. Moore & T. T. Trent

Authors
  1. R. L. Moore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. T. Trent
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moore, R.L., Trent, T.T. Factorization along commutative subspace lattices. Integr equ oper theory 25, 224–234 (1996). https://doi.org/10.1007/BF01308632

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01308632

AMS Classification Number

Search

Navigation