INVERTIBLE INTERPOLATION PROBLEMS IN ALG(equation omitted)

Abstract

In this article, we investigate invertible interpolation problems in Alg(equation omitted) : Let(equation omitted) be a subspace lattice on a Hilbert space H and let X and Y be operators acting on H. When does there exist an invertible operator A in Alg(equation omitted) such that AX = Y?

Keywords

• subspace lattice;
• Alg(equation omitted);
• interpolation problem;
• invertible interpolating operator

File

Download PDF

References

1. Math. Proc. Cambridge Philos Soc. v.111 no.1 Interpolation problems for ideals in certain reflexive operator 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 on Hilbert space R.G.Douglas https://doi.org/10.1090/S0002-9939-1966-0203464-1
3. Indiana University 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 Hilbert-Schmidt interpolation in CSL algebras A.Hopenwasser
5. Interpolation Problems in AlgL Y.S.Jo;J.H.Kang
6. J. Operator Theory v.29 no.1 Interpolation in nest algebras and applications to operator Corona Theorems E.Katsoulis;R.L.Moore;T.T.Trent
7. 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
8. J. Math. Anal. Appl. v.140 no.2 Compact causal data interpolation N.Munch https://doi.org/10.1016/0022-247X(89)90074-7