Let H be a separable Hilbert Space. Denote by H1 = L2(a,b; H) the set of function defned on the interval a < chi < b (<FONT FACE=Symbol>&frac34;</FONT><FONT FACE=Symbol>¥</FONT> <FONT FACE=Symbol>a < c</FONT> < b <FONT FACE=Symbol>&pound;</FONT><FONT FACE=Symbol>¥</FONT>) whose values belong to H strongly measurable [12] and satisfying the condition If the inner product of function <FONT FACE=Symbol>&brvbar;</FONT>(chi) and g(chi) belonging to H1 is defined by then H1 forms a separable Hilbert space. We study separation problem for the operator formed by <FONT FACE=Symbol>&frac34;</FONT> y"+ Q (chi) y Sturm-Liouville differential expression in L2(<FONT FACE=Symbol>&frac34;</FONT> <FONT FACE=Symbol>¥</FONT>, <FONT FACE=Symbol>¥</FONT>; H) space has been proved where Q (chi) in an operator which transforms at H in value of chi,,self-adjoint, lower bounded and its inverse is complete continous