DOI QR코드

DOI QR Code

SOLVING OPERATOR EQUATIONS Ax = Y AND Ax = y IN ALGL

LEE, SANG KI;KANG, JOO HO

  • 투고 : 2014.12.20
  • 심사 : 2015.03.09
  • 발행 : 2015.05.30

초록

In this paper the following is proved: Let L be a subspace lattice on a Hilbert space H and X and Y be operators acting on a Hilbert space H. If XE = EX for each E ${\in}$ L, then there exists an operator A in AlgL such that AX = Y if and only if sup $\left{\frac{\parallel{XEf}\parallel}{\parallel{YEf}\parallel}\;:\;f{\in}H,\;E{\in}L\right}$ = K < $\infty$ and YE=EYE. Let x and y be non-zero vectors in H. Let Px be the orthogonal pro-jection on sp(x). If EPx = PxE for each E $\in$ L, then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y. (2) < f, Ey > y =< f, Ey > Ey for each E ${\in}$ L and f ${\in}$ H.

키워드

Interpolation Problem;Subspace Lattice;AlgL;CSL-AlgL

참고문헌

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