# ON OPERATOR INTERPOLATION PROBLEMS

• Published : 2004.05.01

#### 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.

#### References

1. 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
2. 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
3. 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
4. Illinois J. Math. v.33 no.4 Hibert-Schmidt Interpolation in CSL-Algebras A.Hopenwasser
5. Interpolation problems in AlgL Y.S.Jo;J.H.Kang
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