Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지

UNITARY INTERPOLATION ON AX = Y IN A TRIDIAGONAL ALGEBRA ALG𝓛

  • JO, YOUNG SOO (Dept. of Math., Keimyung University) ;
  • KANG, JOO HO (Dept. of Math., Daegu University) ;
  • PARK, DONGWAN (Dept. of Math., Keimyung University)
  • Received : 2005.08.10
  • Accepted : 2005.09.30
  • Published : 2005.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

Given operators X and Y acting on a separable complex Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. We show the following: Let $Alg{\mathcal{L}}$ be a subspace lattice acting on a separable complex Hilbert space ${\mathcal{H}}$ and let $X=(x_{ij})$ and $Y=(y_{ij})$ be operators acting on ${\mathcal{H}}$. Then the following are equivalent: (1) There exists a unitary operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that AX = Y. (2) There is a bounded sequence {${\alpha}_n$} in ${\mathbb{C}}$ such that ${\mid}{\alpha}_j{\mid}=1$ and $y_{ij}={\alpha}_jx_{ij}$ for $j{\in}{\mathbb{N}}$.

Keywords

References

  1. Operator Theory: Adv. Appl. v.2 Commutants modulo compact operators of certain CSL algebras Gilfeather, F.;Larson, D.
  2. Indiana University Math. J. v.29 The equation Tx = y in a reflexive operator algebra Hopenwasser, A.
  3. Illinois J. Math. v.33 no.4 Hilbert-Schmidt interpolation in CSL algebras Hopenwaser, A.
  4. Pacific J. Math. v.140 Isometris of Tridiagonal algebras Jo, Y.S.
  5. Michigan Math. J. v.37 Isomorphisms of $AlgL_{n}\;and\;AlgL_{\infty}$ Jo, Y.S.;Choi, T.Y.
  6. J. of K. M. S. Equations AX = Y and Ax = y in AlgL Jo, Y.S.;Kang, J.H.;Park, Dong-Wan
  7. J. Operator Theory v.29 Interpolation in nest algebras and applications to operator Corona Theorems Katsoulis, E.;Moore, R.L.;Trent, T.T.
  8. Proc. Nat. Acad. Sci. U.S.A. Irreducible Operator Algebras Kadison, R.
  9. Proc. London Math. Soc. v.19 no.3 Some properties of nest algebras Lance, E.C.
  10. J. Math. Anal. Appl. v.140 Compact causal data interpolation Munch, N.