On the existence of a cyclic vector for some families of operators |
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Authors: | E V Lytvynov |
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Institution: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev |
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Abstract: | Under certain restrictions, it is proved that a family of self-adjoint commuting operatorsA=(A
)![phiv](/content/j0ul1114050j5517/xxlarge981.gif) ![epsi](/content/j0ul1114050j5517/xxlarge949.gif) where is a nuclear space, possesses a cyclic vector iff there exists a Hubert spaceH ![PHgr](/content/j0ul1114050j5517/xxlarge934.gif) of full operator-valued measureE, where ![PHgr](/content/j0ul1114050j5517/xxlarge934.gif) is the space dual to andE is the joint resolution of the identity of the familyA.Published in Ukrainskii Matematicheskii Zhurnal, Vol.45, No. 10, pp. 1362–1370, October, 1993. |
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