# UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

• Kang, Joo-Ho (Department of Mathematics Taegu University) ;
• Jo, Young-Soo (Department of Mathematic Keimyung University)
• Published : 2002.07.01
• 64 20

#### Abstract

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for the n-operators satisfies the equation AX$\_$i/ : Y$\_$i/, for i = 1, 2 …, n. In this article, we obtained the following : Let X = (x$\_$ij/) and Y = (y$\_$ij/) be operators acting on H such that $\varkappa$$\_$ i$\sigma$ (i)/ 0 for all i. Then the following statements are equivalent. (1) There exists a unitary operator A in Alg(equation omitted) such that AX = Y and every E in (equation omitted) reduces A. (2) sup{(equation omitted)}<$\infty$ and (equation omitted) = 1 for all i = 1, 2, ….

#### Keywords

interpolation problem;subspace lattice;unitary interpolation problem;Alg(equation omitted)

#### References

1. 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