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UNITARY INTERPOLATION PROBLEMS IN CSL-ALGEBRA ALGL

  • Jo, Yong-Soo (Department of Mathematics, Keimyung University) ;
  • Kang, Joo-Ho (Department of Mathematics, Taegu University)
  • Published : 2003.05.01

Abstract

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. An interpolating operator for n-vectors satisfies the equation Ax$_{i}$=y$_{i}$. for i=1,2, …, n. In this article, we investigate unitary interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H. Let x and y be vectors in H. When does there exist a unitary operator A in AlgL such that Ax=y?

Keywords

Unitary interpolation problem;subspace lattice;CSL-algebra AlgL

References

  1. Illinois J. Math. v.33 no.4 Hilbert-Schmidt interpolation in CSL algebras A.Hopenwasser
  2. Invertible Interpolation problems in CSL-Algebra AlgL Y.S.Jo;J.H.Kang
  3. J. Operator Theory v.29 Interpolation in nest algebras and applications to operator Corona Theorems E.Katsoulis;R.L.Moore;T.T.Trent
  4. J. Math. Anal. Appl. v.140 Compact causal data interpolation N.Munch https://doi.org/10.1016/0022-247X(89)90074-7
  5. Interpolation problems in CSL-Algebra AlgL to appear in Rocky Mountain Journal Y.S.Jo;J.H.Kang
  6. Proc. London Math. Soc. v.19 no.3 Some properties of nest algebras E.C.Lance https://doi.org/10.1112/plms/s3-19.1.45
  7. Proc. Nat. Acad. Sci. U.S.A. Irreducible operator algebras R.Kadison
  8. Indiana Univ. Math. J. v.29 The equation Tx = y in a reflexive operator algebra A.Hopenwasser https://doi.org/10.1512/iumj.1980.29.29009