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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제33권 제3호
- 발행연도
- 2015.1
- 수록면
- 417 - 424 (8page)
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In this paper the following is proved: Let <italic>L</italic> be a subspace lattice on a Hilbert space <italic>H</italic> and <italic>X</italic> and <italic>Y</italic> be operators acting on a Hilbert space <italic>H</italic>. If <italic>XE</italic> = <italic>EX</italic> for each <italic>E</italic> ${\in}$ <italic>L</italic>, then there exists an operator <italic>A</italic> in Alg<italic>L</italic> such that <italic>AX</italic> = <italic>Y</italic> 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 <italic>x</italic> and <italic>y</italic> be non-zero vectors in <italic>H</italic>. Let <italic>P<sub>x</sub></italic> be the orthogonal pro-jection on <italic>sp</italic>(<italic>x</italic>). If <italic>EP<sub>x</sub></italic> = <italic>P<sub>x</sub>E</italic> for each <italic>E</italic> $\in$ <italic>L</italic>, then the following are equivalent. (1) There exists an operator <italic>A</italic> in Alg<italic>L</italic> such that <italic>Ax</italic> = <italic>y</italic>. (2) < <italic>f</italic>, <italic>Ey</italic> > <italic>y</italic> =< <italic>f</italic>, <italic>Ey</italic> > <italic>Ey</italic> for each <italic>E</italic> ${\in}$ <italic>L</italic> and <italic>f</italic> ${\in}$ <italic>H</italic>.
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