Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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NORMAL INTERPOLATION PROBLEMS IN ALGL

  • Published : 2004.10.01
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Abstract

Let X and Y be operators acting on a Hilbert space and let (equation omitted) be a subspace lattice of orthogonal projections on the space containing 0 and I. We investigate normal interpolation problems in Alg(equation omitted): Given operators X and Y acting on a Hilbert space, when does there exist a normal operator A in Alg(equation omitted) such that AX = Y?

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References

  1. M. Anoussis, E. Katsoulis, R. L. Moore, and T. T. Trent, Interpolation problems for ideals in certain reflexive operator algebras, Math. Proc. Cambridge Philos. Soc. 111 (1992), 151-160. https://doi.org/10.1017/S030500410007523X
  2. R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-415. https://doi.org/10.1090/S0002-9939-1966-0203464-1
  3. A. Hopenwasser, The equation Tx = y in a reflexive operator algebra, Indiana Univ. Math. J. 29 (1980), 121-126. https://doi.org/10.1512/iumj.1980.29.29009
  4. A. Hopenwasser, Hilbert-Schmidt interpolation in CSL algebras, Illinois J. Math. 33 (1989), no. 4, 657-672.
  5. Y. S. Jo and J. H. Kang, Interpolation Problems in AlgL, to appear.
  6. E. C. Lance, Some properties of nest algebras, Proc. London Math. Soc., 3 19 (1969), 45-68. https://doi.org/10.1112/plms/s3-19.1.45
  7. N. Munch, Compact causal data interpolation, J. Math. Anal. Appl. 140 (1989), 407-418. https://doi.org/10.1016/0022-247X(89)90074-7