# 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)
• Published : 2004.05.01
• 95 5

#### Abstract

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.

#### Keywords

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

#### References

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
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