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SELF-ADJOINT INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

  • Kang, Joo-Ho (Department of Mathematics, Taegu University) ;
  • Jo, Young-Soo (Department of Mathematics, Keimyung University)
  • Published : 2002.08.01

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 n-operators satisfies the equation $AX_{}i$ = $Y_{i}$ for i/ = 1,2,…, n. In this article, we obtained the following : Let X = ($x_{i\sigma(i)}$ and Y = ($y_{ij}$ be operators in B(H) such that $X_{i\sigma(i)}\neq\;0$ for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup ${\frac{\parallel{\sum^n}_{i=1}E_iYf_i\parallel}{\parallel{\sum^n}_{i=1}E_iXf_i\parallel}n\;\epsilon\;N,E_i\;\epsilon\;L and f_i\;\epsilon\;H}$ < $\infty$ and $x_{i,\sigma(i)}y_{i,\sigma(i)}$ is real for all i = 1,2, ....

Keywords

References

  1. J. Functional analysis v.3 Interpolation problems in nest algebras W. B. Arveson
  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. Operator Theory: Adv. Appl. v.2 Commutants modulo the compact operators of certain CSL algebras F. Gilfeather;D. Larson https://doi.org/10.1007/978-3-0348-5456-6_9
  4. 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
  5. Illinois J. Math. v.33 Hilbert-Schmidt interpolation in CSl algebras A. Hopenwasser
  6. Pacific Journal of Mathematics v.140 no.1 Isometries of Tridiagonal Algebras Y. S. Jo https://doi.org/10.2140/pjm.1989.140.97
  7. Michigan Math. J. v.37 Isomorphisms of $AlgL_n$ and $AlgL\infty$ Y. S. Jo;T. Y. Choi https://doi.org/10.1307/mmj/1029004137
  8. Rocky Mountain Journal of Math. Interpolation problems in CSL-Algebra AlgL Y. S. Jo;J. H. Kang
  9. Proc. Nat. Acad. Sci. U.S.A. Irreducible Operator Algebras R. Kadison
  10. J. Operator Theory v.29 Interpolation in nest algebras and applications to operator corona theorems E. G. Katsoulis;R. L. Moore
  11. Proc. London Math. Soc. v.19 Some properties of nest algebras E. C. Lance https://doi.org/10.1112/plms/s3-19.1.45
  12. Aarhus University reprint series no.11 Compact causal data interpolation N. Munch