一类CSL代数的插值问题

INTERPOLATION PROBLEMS OF CERTAIN CSL ALGEBRAS

设Ｌ为Ｈｉｌｂｅｒｔ空间Ｈ中的子空间格．给定Ｘ，Ｙ∈Ｂ（Ｘ），何时必有算子Ａ∈ａｌｇＬ，使得ＡＸ＝Ｙ？本文在一类ＣＳＬ代数中讨论该问题．另外，我们也考虑ＣＳＬ代数中形如ｎｉ＝１ＡｉＸｉ＝Ｙ１的插值问题．本文推广了［５］和［７］中的一些结果，并有新的结论．

Let L be a subspace lattice in Hilbert space H. Given X, Y∈B(H), when there is an operator A∈alg L such that AX=Y? E.Katsoulis gave a necessary and sufficient condition in nest algebras. In this paper, we discuss this problem in certain CSL algebras and get a similar result. In addition, we consider the interpolation problem with the form n i=1 A iX i=Y 1 in these CSL algebras, and thereby generalize the main results of Arveson in .