DOI QR코드

DOI QR Code

ON OPERATOR INTERPOLATION PROBLEMS

  • Jo, Young-Soo (Department of Mathematics Keimyung University) ;
  • Kang, Joo-Ho (Department of Mathematics Daegu University) ;
  • Kim, Ki-Sook (Department of Mathematics Daegu University)
  • 발행 : 2004.05.01

초록

In this paper we obtained the following: Let H. be a Hilbert space and (equation omitted) be a subspace lattice on H. Let X and Y be operators acting on H. If the range of X is dense in H, then the following are equivalent: (1) there exists an operator A in Alg(equation omitted) such that AX = Y, (2) sup (equation omitted) Moreover, if condition (2) holds, we may choose the operator A such that ∥A∥ = K.

키워드

interpolation problem;subspace lattice;Alg(equation omitted);CSL.

참고문헌

  1. Illinois J. Math. v.33 no.4 Hibert-Schmidt Interpolation in CSL-Algebras A.Hopenwasser
  2. 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
  3. 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
  4. Interpolation problems in AlgL Y.S.Jo;J.H.Kang
  5. Math. Proc. Camb. Phil. Soc. v.111 Interpolation problems for ideals in nest algebras M.Anoussis;E.Katsoulis;R.L.Moore;T.T.Trent https://doi.org/10.1017/S030500410007523X
  6. J. Math. Anal. Appl. v.140 Compact causal data interpolation N.Munch https://doi.org/10.1016/0022-247X(89)90074-7
  7. Pro. Nat. Acad. Sci. U.S.A. Irreducible Operator Algebras R.Kadison
  8. Proc. Amer. Math. Soc. v.128 no.3 Linear equations in subspaces of operators R.Moore;T.T.Trent https://doi.org/10.1090/S0002-9939-99-05064-9
  9. J. Operator Theory v.29 Interpolation in nest algebras and applications to operator Corona Theorems E.Katsoulis;R.L.Moore;T.T.Trent
  10. Proc. Amer. Math. Soc. v.17 On majorization, factorization, and range inclusion of operators of Hilbert space R.G.Douglas https://doi.org/10.2307/2035178

피인용 문헌

  1. SOLVING OPERATOR EQUATIONS Ax = Y AND Ax = y IN ALGL vol.33, pp.3_4, 2015, https://doi.org/10.14317/jami.2015.417
  2. COMPACT INTERPOLATION ON AX = Y IN ALG𝓛 vol.32, pp.3_4, 2014, https://doi.org/10.14317/jami.2014.441
  3. NORMAL INTERPOLATION ON AX = Y IN ALG$\mathcal{L}$ vol.30, pp.2, 2008, https://doi.org/10.5831/HMJ.2008.30.2.329